Their marriage records should give the fathers' names and occupations - which is usually the easiest source to locate.

A grandparent's will sometimes names an illegitimate child of a son. Father's wills also quite often name illegitimate children.

Sometimes they turn up in a census with a grandparent (father's parent), or other relative of the father. I'd check them in each census.

It makes the search easier when the surnames have been given.

Sue