THE FIFTEENTH DEGREE

That was Henri Matisse telling himself he would do whatever pleased him without thinking about what others demanded of him, and I liked where he was coming from. He'd just survived a tricky surgical procedure when he said it; I was on the cusp of having survived the rigours of cycling across two countries. I could sympathise, kind of.

I was in the town of Le Cateau-Cambrésis. Henri had been born there on New Year's Eve 1869 but, after a stint in Paris, spent much of his life on the French Riviera, where he died in 1954. He clearly had a soft spot for Le Cateau-Cambrésis, however, as he established a museum in the town with a donation of 82 of his works. It was a pity he never saw fit to establish a campsite. The polite lady in the tourist office broke the news gently.

'I'd have liked to visit the museum but with all my luggage on the bike, I don't want to leave it out in the street,' I pined.

'You can leave your bike here if you like,' she suggested.

Now that's customer service.

The museum was somewhat livelier than your average art museum. Groups of primary school children were on their end-of-year outing. They gave me bemused looks as I wandered amongst them in my cycling apparel. With Matisse's penchant for depicting large expanses of human flesh in his paintings, perhaps they had me down as one of his models. It may even have been one of the tasks on their clipboard: 'Locate and stare for a few seconds at someone who could feasibly have been painted by the artist.' Tick.

Next up was Maubeuge. I had stayed at Le Grand Hôtel in Maubeuge in 2010 as I cycled to southern Italy and had likened the experience to spending the night at the Moulin Rouge nightclub in Paris. Before you get too excited, this was entirely down to the decor rather than any form of entertainment on offer. Opposite the hotel, I found the bar where I had stopped for a beer nearly five years previously. Should I opt for a second night at Le Grand?

Ten minutes later I was at the reception desk of the Ibis hotel down the road, where I hoped that the colour scheme wouldn't keep me awake at night.

'I don't have a booking in your name, monsieur,' the hotel employee informed me.

'I have it here on my phone,' I offered.

'I can't deal with you until we have received the reservation email,' she retorted, sternly.

'So, what shall I do?' I asked, wanting to be annoying and knowing full well that in Maubeuge there weren't that many options.

'You can wait here,' she snapped.

'Will there be a place to store my bike?'

'Yes, it's a non-motorised vehicle with two wheels,' I quipped.

The receptionist, perhaps justifiably, ignored me.

The email did eventually arrive and I had the pleasure of overpaying for a bog-standard room in a hotel with a dubious level of cycle friendliness. But who cared? I was sure that however much cycling displeasure the Ibis corporation could muster, it would be more than compensated for by Belgium, now just a few kilometres away and home to the one and only European Cyclists' Federation (ECF), the people in charge of the EuroVelos.

Several years previously, I had contacted the organisation to request information and was put in touch with Kevin Mayne, their development director. He was once the chief executive of Britain's CTC, the Cyclists' Touring Club – or, as it has now been rebranded, Cycling UK. Knowing that I would be passing near Brussels, I contacted Kevin again and asked if he would be interested in meeting up. He was, and not only did he agree to cycle with me for some of my route through Belgium, but he also offered to put me up for a couple of nights. A guided visit to the nearby battlefield of Waterloo was also on the cards for the next rest day. It was good to have friends in reasonably high places.

Kevin had told me that after following the River Sambre over the unmarked Belgian border, I should follow a series of RAVeL paths. These were randonnée-vélo or 'walking-cycling' routes and within a few minutes of arriving in what I assumed to be Belgium, I started to notice the distinctive numbered RAVeL signs. A combination of RAVeLs 101 and 108 got me as far as Binche and thereafter it was the 422 to my meeting point with Kevin in the centre of the town of La Louvière.

My mobile phone hadn't rung once since leaving Tarifa so when it did, I assumed that the unrecognised number was that of Kevin.

'I'm in the main square. Look out for a red-brick church,' he explained.

This being Belgium, there were plenty of red-brick buildings to choose from but I quickly located a church – red brick, of course – in a square. A few homeless people were gathered near the entrance. Unless the ECF had hit bad times rather abruptly, I guessed he wasn't one of them. Nearby, a man with a bright orange armband was escorting a group of children across the road.

'Excuse me,' I said, 'is this the main square in La Louvière?'

'This isn't La Louvière,' he replied.

I put the man down as Belgium's leading pedant as, in fairness, when I did find Kevin in a similar square outside a similar redbrick church a few minutes later, I hadn't cycled that far.

Our common love of all things cycling on a European level made for easy conversation with Kevin over a coffee. We had 45 km to cycle but this was an area that he knew well, and he was familiar with all the twists and turns of the cycle paths. I cycled in his wake and was afforded the time to enjoy the pretty views along the canals, rivers and country lanes of Wallonia, the French-speaking lower half of Belgium. The route wasn't devoid of hills or indeed cobbles but by early evening, as the warm sun of late spring was on its final trundle towards the horizon, we arrived at Kevin's house in Chapelle-Saint-Lambert, about 25 km south of Brussels.

My own credentials to claim to be a 'proper' cyclist were somewhat dubious. My lack of technical knowledge, my inability to name men who have won the Tour de France but aren't called Bradley or Chris, my fading desire to wear black Lycra: none of these worked in my favour. Neither did my ownership of (give me a moment to count...) just one bicycle. Yes, one.

I regularly meet people who have more than one bike, usually two – one for racing, one for everything else – but often three (a mountain bike) and sometimes four (a rusting 'project' bike perhaps). Kevin had 12. The milking parlour next to the house he shared with his Kiwi wife, Cheryl, wasn't so much a bike shed as a bike archive. According to his biography on the ECF website, his collection consisted of 'two city/hybrids for daily use, two MTBs, two road bikes, two touring bikes, two fixies and a Chinese Flying Pigeon'*. That was only 11. Kevin had clearly put into practice the old cycling adage that if n is the number of bikes that you own, n + 1 is the number of bikes that you need.

In the morning it was rest day number six and it was time to catch up again, perhaps for the last time, with Napoléon – the original one, not his nephew of phoney-castle fame – at the place where he met his Waterloo at, err… Waterloo. When Monsieur B. escaped from Elba in February 1815, marched through France to Paris, overthrew the government and regained power, the rest of Europe wasn't best pleased. The issue was brought to a climax in June 1815 just south of the town of Waterloo, in modern-day Belgium. Napoléon and his armies were defeated; he tried but failed to escape to the United States and ended up as a prisoner on Saint Helena. And didn't escape.

My arrival in Belgium in late May 2015 was 199 years and 11 months after Napoléon's. Big commemorations were being planned for the two-hundredth anniversary of the battle on 18 June and, as Kevin and I approached the site on our bikes, large stands were being erected around the wide dip in the land where the event had taken place. High-level dignitaries were expected to attend a largescale re-enactment. One of the stands appeared to be facing in the wrong direction.

'Is that for the French delegation?' I enquired. Kevin wasn't sure.

At the end of the day, a field is a field. Of more interest were the attractions on the north-western side of the battlefield. There were three and they each represented a different approach to telling the story of Waterloo.

First up was the Lion's Mound, built by the Dutch a decade after the battle and standing 43 m above ground. On top of the mound was an iron statue of a lion, symbol of the monarchy of the Netherlands. It was on this spot that William II fell from his horse after having been shot. Poor bloke. A fitting tribute. But hang on… He wasn't killed. It was a mere flesh wound. He wasn't even king at the time. I wondered how much bigger the mound might have been if he hadn't survived. That said, the view from the top was worth the climb of 225 steps. If you had been a visitor when the mound was finished in 1826, I dare say there would have still been a good number of people around who could have provided a first-hand account of the battle. Where better to listen to their recollections than on top of a man-made hill looking down upon the battlefield?

By the time of the first centenary of the battle, in 1915, Europe was once again at war. The decision to paint a panoramic fresco of the battle and house it in a rotunda at the base of the mound in 1912 was a timely one. If it had been left for a few more years, priorities may have been elsewhere.

But the sensory-hungry child of the twenty-first century demands more: 3D video, multimedia walls, buttons that can be pushed… Which is why, to commemorate the bicentenary of Waterloo, a third attraction has now been added. It's no longer de rigueur to build mounds or rotundas next to famous battlefields, so the Memorial 1815 is buried underground. Over 1,815 square metres (can you see what they'd done there?), it '... allows you to experience one of the most turbulent times in our history… as if you were there.' And it did. Indeed, the combination of mound, panorama and 'multi-sensory experience' sets a mighty challenge for the museum curators and architects of the early twenty-second century in the run-up to the tri-centenary.

Kevin and I cycled back to his house via Hougoumont Farm – a key point of the fighting – and what remained of the day was spent relaxing, eating, drinking and doing a little shopping. With his superior technical knowledge, Kevin gave Reggie the once-over and everything seemed fine. Over the course of the cycle through northern France, the annoying click had returned. It hadn't been the bottom bracket after all but as to what was causing the noise, both Kevin and I remained ignorant.

My original plan had been to cycle through southern Belgium and over the border to Germany. Kevin's house, however, was a little further north than I had envisaged. I sat with my host to discuss route options over breakfast and he suggested that I cycle to Leuven and then head east to Maastricht. This wasn't a problem, far from it. Maastricht was in the Netherlands and my continental journey had just been elevated from a seven- to an eight-country odyssey.

Kevin supplied me with a couple of maps and explained the system of nodes, which is popular across the Low Countries. Whenever two cycle paths – of which there were many – crossed, the junction was attributed a two- or three-digit number. My cycle between Leuven and Borgloon could be summarised as follows: 33, 73, 87, 86, 92, 91, 34, 35, 13, 64, 60, 59, 58, 50, 21, 51, 187, 188, 135, 189, 168, 169, 161, 151, 154, 152. How wonderful was that? Following the numbers was easy and, aside from one slight hiccup when crossing the town of Sint-Truiden (between 189 and 168), I was able to follow good-quality off-road cycle paths for almost all of the day.

I'd planned to stay overnight in Sint-Truiden but I wasn't able to locate a campsite or a reasonably priced hotel. I might have bitten the financial bullet and stayed put had it not been for the drunks inside the bar where I stopped. One customer was ranting at the counter, the woman serving me laughed mockingly when I asked if she spoke English and then a drinker, who did, proceeded to tell me that 'British beer is crap.'

I searched online accommodation options further along the line and at 152 was a nice-looking B&B called the Huis Van Loon. The house of the Loons? It sounded like the bar I had been sitting in but I was willing to give it the benefit of the doubt. It was an excellent call as not only was the B&B rather wonderful, but so was the cycle in the early evening sun through the fruit farms to the west of Borgloon. I celebrated the end of my final full day of cycling in Belgium with an 8 per cent blonde beer at the Goede Ogenblik – 'good moment' – bar. A good moment indeed.

Cycling day 41 was brought to you by knooppunts (that's 'nodes' to you and me) 136, 139, 128, 129, 107, 111, 112, 113 and 86. The downside of node following was that I didn't need to refer to the map every few minutes and the towns and villages passed by anonymously. The upside was that I had more opportunity to appreciate the land and townscapes around me, and in the case of Dutch-speaking Flanders, there was much to appreciate.

After Belgium node 86 I was required to consult the map. The pencil-straight N79 would take me to Maastricht in the Netherlands quicker than a Eurosceptic with a blowtorch. Fuelled by a large bag of Engelse drop (liquorice allsorts), within half an hour I had arrived at a high bridge over the Meuse Canal where a small memorial was dedicated to British and Belgian soldiers who had died fighting here. Although a very modern construction, the foundations of the bridge were distinctly 1940s, with the bunker on one side having been converted into a swish restaurant. A 'World Peace Flame' was burning behind the reinforced glass of a display cabinet. Everything pointed to me having arrived at an international border but, according to my online map, I would have to cycle for another 250 metres on the other side of the canal to arrive at the point where Belgium became the Netherlands. When it arrived, the border was indicated only by a small sign noting that I was now in Maastricht. It was almost too understated.

Cycling along what had now been renamed the N278 was the stuff of dreams. For the first time in my life, I, a cyclist, really did feel as though I was being treated as an equal to the motorist. The 3 km stretch of road from the border to the centre of the city contained all the features that British councils like to list in their glossy 'Cycling Strategy for the Twenty-first Century'-type brochures but never seem to get around to implementing. Segregation and space. Traffic signals for those on two wheels. Separate outer roundabouts with clearly marked priority to bicycles. Cycle lanes clear of street furniture. Two-way cycling on otherwise one-way streets. Hectares of secure bicycle storage. And guess what, petrolheads? Not one cyclist ignoring a red light. No helmet cams recording evidence of bad driving. Just two forms of transport functioning harmoniously side by side. It was as delightful to witness as it was frustrating to reflect upon just how far the British have yet to travel.

Maastricht was more modern than I had imagined. The city had much that was old but also much that was very new. This included a large shopping centre where I stocked up on food for the evening before completing the day's cycle by heading south along the banks of the Meuse to Camping De Oosterdriessen, where I settled in for the evening. Another tent had already been erected in the free camping area. Its occupant returned on his bike a little later. He seemed familiar and appeared to recognise me too: 'Weren't you at the campsite in Orléans?' he asked in what sounded like a Spanish accent. It turned out that he was the guy with whom I had exchanged brief nods on the morning of my departure.

Javier was from Argentina; he was also the first cyclist I had met who was heading to Nordkapp. We had much to discuss.

Javier's approach to cycling to the northernmost point of Europe – from Madrid – was a little more laid-back than my own. He'd picked up his bike second-hand and quite cheaply in Spain, equipped himself with eBay-purchased kit, and had no apparent time limit to his adventure. With a Spanish passport courtesy of a grandparent, he had no Schengen-limited visa, and explained that he was stopping to work and earn money from time to time. Back in Argentina he had been a chef for several years so, along with a decent level of English, he certainly had a skill that would find him work almost anywhere he went. I envied his Laurie Lee approach to travelling.

The following morning, an hour or so into the cycle across this most southerly and narrowest part of the Netherlands, I started to notice signs for a nearby American war cemetery. When I spotted the entrance, I decided to investigate and, set back a few hundred metres from the road, I found 8,301 headstones of American soldiers killed in action.

My mind immediately returned to the sombre atmosphere of the German cemetery I had visited in France. Despite the grand buildings in marble, there was nothing triumphal about what I could see here. There was, however, an uplifting and hopeful atmosphere that had been absent from the German cemetery. I gazed along the geometrically perfect lines of crosses. The men in the graves before me died in ignorance of the ultimate demise of the Third Reich, and the downfall of Hitler and the Nazis. They died hoping but not knowing. It was a strange, disconcerting thought.

Something rather special was about to happen. No, it wasn't that I was able to buy a punnet of strawberries from a vending machine beside the road (although I did have fun doing so). It was that, for the first time since leaving Gibraltar – now over 3,000 km of cycling to the south – an international border was being signposted and celebrated.

The celebration came in the form of a bush with the black eagle of the Federal Republic of Germany embedded neatly into its side.

If all this wasn't sufficient to excite me, 500 metres further down the road was a second sign welcoming me to Aachen. Alongside the multilingual welcomes was a list of eight Partnerstädte, or twin towns: Arlington in Virginia, Kostroma in Russia, Montebourg in France, Naumburg in Germany (presumably a hangover from the DDR days), Ningbo in China, Reims in France (another one? Was that allowed?), Toledo in Spain and Halifax/Calderdale, my hometown in the United Kingdom.

I hadn't been aware of Aachen's twinning infidelities across the globe but I had always known of the Aachen–Halifax connection. Indeed, one of the first foreigners I ever met was a German Boy Scout called Karsten who stayed with my family for a weekend back in the late 1970s. He was taking part in an exchange between Scouts in Halifax and Aachen, spoke good English and was very tall. This latter aspect of Karsten's physique formed a lasting impression on a small boy from the Calder Valley of Yorkshire. He will now be in his fifties and must, without a doubt, be in charge of something important in North Rhine-Westphalia.

Ten minutes later, after pausing to take a picture of Halifaxstraβe, I was in the city centre. Four countries in five days was good going, although admittedly the jigsaw geography of this corner of Western Europe was aiding me somewhat. However, I wouldn't be crossing another border for probably a couple of weeks. The plan was to cycle over to the Rhine at Cologne and then head north to Düsseldorf. Keeping towards the western side of the country, I envisaged passing through Münster and Bremen before visiting friends in Hamburg. The final portion of Germany would be through Schleswig-Holstein.

Aachen's campsite, I was informed by the formal woman in the tourist office, didn't allow camping. Well, not my kind of camping – just 'camping' in a motorhome. Which isn't, can I say, camping. I'm glad I've got that off my chest. I booked into the central Hotel Klenkes instead and was allocated a room that would have given the proverbial cat severe head injuries. I escaped the cramped conditions and went to explore the rather more spacious cathedral.

Its ordinary exterior belied extraordinariness within. Built for Charlemagne in the eighth century, it contained not only the first domed church to be built north of the Alps, but enough shimmering gold leaf to keep Hatton Garden supplied for decades. Byzantine was the style: exotic domes, tall rounded arches and rich mosaics. Especially impressive when you consider that it had survived for such a long time. The building had been host to coronations for six centuries, the final one being that of Ferdinand I in 1531, after which point the centre of gravity of the Holy Roman Empire moved east towards what is now Austria.

Along similar lines, my own centre of gravity also needed to move east. Cycling day 43 consisted of an 80 km descent into the Rhine valley that dominated this part of Germany and which I would follow north until at least Düsseldorf.

My arrival in the centre of Cologne coincided with the discovery of another visitor from Britain. My compatriot had been in hiding for over 70 years and had just been discovered near the Mülheim Bridge. The BBC website broke the news thus:

Some 20,000 people in the German city of Cologne have been forced to leave their homes as authorities defuse a one-tonne bomb from World War Two. Schools and kindergartens – as well as the zoo – remained closed during the city's largest post-war evacuation.

I would need to cycle near the Mülheim Bridge the following morning so I could only hope that things had been sorted out by then. There was no sign of any form of panic in central Cologne, however. Indeed, when I met with my friend Janina, a former language assistant from the school in Henley, and mentioned the news to her, it was the first she had heard of the event.

I had initially suggested that we go out for a meal in the evening but Janina explained that she had to go to a concert. I had always considered her to be an educated, cultured woman and assumed that whatever event she was attending, it would involve classical music or perhaps even opera. I wouldn't have been at all surprised if she herself had been one of the performers.

'Sorry about tonight,' she explained, 'but I've had these Olly Murs tickets for ages.'

Turned down for Olly Murs. That put me in my place.

The campsite in Cologne was a few kilometres to the south of the city, on the other side of the river. It consisted of an open patch of land where a good number of independent travellers, many on two wheels, were enjoying the fresh air. The noise from the nearby bridge was a touch distracting but at least it wasn't at risk of being blown up by an RAF bomb, or so I assumed.

The combination of a day off, two short cycling days and a predominantly eastward shift had made the fifteenth degree the longest yet in terms of time. But now that I had reached the Rhine, there would be an abrupt change of direction and I would again be able to make more significant progress north. The next section of cycling would be easy, as it was simply a case of following the Rhine Cycle Route, otherwise known as EuroVelo 15 to Düsseldorf. I had already seen several signs for the route, as it passed outside the gates of the campsite. I saddled up and, via a short detour back into the centre of Cologne for breakfast and to take in the cathedral, I was off. Einfach!**