I don't know anything about Thomas Walker, but I do know the History of Parliament website is far from infallible. In the case of the one MP I've researched (Thomas Bludworth 1620-1682) they do mention his two wives, but they have one name wrong. His birth details are completely wrong, (date, place and father).
But of course trees on Ancestry are even more fallible ...
David
PS. I see now that Thomas is the father of the MP in the article. In that case it would seem quite likely that a second wife would not be mentioned, even if the author knew of her.