Charles Edward Stuart, known during his lifetime as the Young Pretender and later as Bonnie Prince Charlie, did indeed visit London in 1750 and was converted to Protestantism. If he’d hoped it would endear him to the people, the attempt was doomed to failure, and Charles soon returned to his Catholic upbringing.
The visit was known to the authorities and was carefully watched, but they elected to leave him alone, as to arrest him would be to create a Stuart martyr.
Another reason was to court and perhaps marry a British noblewoman. At this stage in the campaign, that would have given Charles a foothold at the heart of power, a strong negotiating counter and access to the money he desperately needed.
The next year, 1751, the popular Prince of Wales, Prince Frederick, died, leaving only a young boy to succeed him, so the Stuart cause looked hopeful again. However, this time they didn’t have a great army at their beck and call, so they had to rely on negotiation and intrigue.
Another Stuart, Lord Bute, helped to thwart the cause by befriending the widowed Princess of Wales and taking over the education of the heir, young Prince George. The Whigs hated him, but after Prince George became King George III, Bute became Prime Minister for a short period.
That story is for another time.
Due to the constant complaints about fortune hunters eloping with heiresses, sometimes abducting them, raping them, and ruining their reputations, the law was changed in 1753, coming into force in 1754. Now marriage was strictly regulated and only valid under the circumstances detailed in the law. Any marriages conducted before that date were valid, if they could be proved.