OK, have you found the person's possible marriage in FreeBMD?
If so, click on page no for the marriage. Registers show two marriages per page (ie four people). Post 1911, the index helpfully tells you which names are matching spouses; if pre, you'll have to guess/try both.
Post 1911, once you've got two surnames you can flog the database for children born with father's name, mother's maiden name, in an interval say 20 years from the marriage.
Pre 1911 it's way harder as you don't have mother's maiden name in the index. You need other info to match. BUT it's still worth looking because you might get something helpful if eg this is the only family called Cholmondley in Leeds, or the Smiths might use Anastasia Gertrude as a family name.
Ancestry has now has some marriage & bapt registers for Manchester, Birmingham, West Yorkshire and London. So if your family is in those locations, a subscription would mean you might get away without ordering certificates to confirm your hunches (and of course will get the censuses, etc).
Otherwise it's certs from the General Record Office at £10 a pop to confirm your hunches.