He's been mangled together with a form of the name of Sir Thomas White of Swanborne (& Aldershot), the birth and death dates, and wife and two of the children, of Thomas (not a knight) White of Somerset, and additional children from I have no idea where.
The daughter Alice has had an extra husband foisted on her, with a long tail of descendants, mostly from Devon. (There certainly were Whites all over the West Country, with known armigerous families in Exeter, Devon; Poole, Dorset; Weymouth, Dorset; and Truro, Cornwall. They all had different arms, which indicates that they were not closely related.)
Most of the extra children seem to be from Bingham in Nottinghamshire, with one from Stourton-le-Steeple (check out the family of Alexander White of that town) and one from Surrey (no idea on that one). The Bingham children seem to belong under "Thomas White, Jr.", but I don't know where *he* belongs.
I think we an take it as read that this Wilton Molford character married *someone* named Alice White - but she wasn't the one who was the daughter of Thomas White of Somerset (she's spoken for, by someone named Coles). Probably yet another hitherto unknown Thomas White, this one from Devon.