Illegitimacy in Victorian England was a great stigma for both mother and child. An illegitimate child would have no claim on its father, and the Bastardy Clause of the 1834 Poor Law set law that said children would be the sole responsibility of the mother.
Of course, there are examples where a father would take care of his children; perhaps the most famous example just prior to this era is the Duke of Clarence, whose mistress, the actress Dorothea Jordan, bore at least ten of his children. The duke ensured his illegitimate children did well in the world, either through marriage for the daughters or occupations for the sons.