DNA matching leads me to believe that this is her (the one age 7) on the 1851 census:
https://www.ancestry.co.uk/imageview...rue&pId=868422
26 Royal St, Lambeth, Surrey
James Aldridge Head Unm 40 Cabinet Maker Gosport
Henry Parker Head Mar 28 Turner & Carver St Georges Surry
Jane Wife Mar 30 Ellisfield Hants
Jane Daughter 7 Walworth Surry
Daniel Keshaw Head Unm 21 Clerk Dublin.
On other censuses, Jane sr's birthplace is Basingstoke, which is my Jane's birthplace on the 1891 census. Surely it can't be a coincidence!
This seems to be the parents' marriage:
https://www.ancestry.co.uk/discovery...=successSource
5 Oct 1886 (not a typo), St John, Waterloo Rd / St John the Evangelist, Lambeth
Henry Parker full age, bachelor, pattern maker & turner, father James Parker, carpenter & turner. Jane Lawrence full age, spinster, father Robert Lawrence, farmer. Both give their residence as 9 Stangate. Marriage by banns. Witnesses Alexr Frazer and Elizabeth Watson.
Henry is in Lambeth on the 1841 census with his father James, a wood turner, and family, and the relatively strong DNA matches that I have found are with descendants of his (presumably half-) siblings.
I haven't found a birth reg or baptism for Jane jr yet though, nor have I found her on the 1861 or 1871 census - she is not with Henry and Jane sr on any census apart from the 1851.