The daughter of Joseph White was definitely Elizabeth
A ...
1861RG9/2226 16 26
Warwick St Nicholas
Factory YardJoseph White, head, wid, 45, Car proprietor, b. Gloucestershire Hidecoat
Elizabeth A, dau, 14, Father's House Keeper, b. Warwick Mary J, dau, 9, don't go to school, b. do.
Sydney J, son, 7, don't go to school, b. do.
Sarah R, dau, 5, scholar, b. do.
1851HO107/2074 109 12
Wellesbourne Hastings, WarwickshireJoseph White, head, 35, Labourer, b. Gloucestershire Hidcote?
Catherine, wife, 20, b. Warwickshire Kenilworth
Thomas, son, 7, b. Warwick
Elizabeth, dau, 4, b. do.
Hmm. Age 20 seems a bit weird

There's a possible marriage March 1868 Kings Norton
Elizabeth Ann White - Thomas Brown In 1871 (they're in Handsworth Staffordshire), it says that Thomas age 32 is from ?Northampton?.
I can see one Catherine Roadknight age 20 on the 1841 census for Wappenbury Warwickshire, but she's not with her family (she's a servant on a farm). Not much help