It seems possible that the fictitious name was Huburn not Davis.
Found a potential match for William's father George Davis. Born 1832 in Handsworth, the son of a Thomas Davis and maybe a Charlotte Smallwood.
They have a number children, the younger ones registered as Davis/Smallwood. However Thomas and Charlotte do not marry until after the birth of 4 or 5 children.
That could mean that they are not Thomas's or not Charlotte's. However one thing in favour of it is that though all the children were born in Handsworth, Thomas and Charlotte married in Edgbaston. Which can point to hiding a late marriage.