Hi RosemH,
There's an obvious candidate on the IGI:
born 10 Aug, baptised 21 Nov 1794 in Howden
Elizabeth Leighton d/o Thomas Leighton & Dorathy Nixon.
It's an entry extracted from the parish records, so I'm not sure if Nixon was Dorathy's maiden name or if the child was illegitimate.
However, there are also 2 other possibles on the IGI:
baptised 1794 in South Cave d/o Samuel & Johannah
baptised 1790 in Hessle by Hull d/o Frances.
The best idea would be to try and find out if Elizabeth survived until the 1851 census when she should have indicated her birthplace.
Otherwise, were any of William & Elizabeth's children named Thomas, Dorothy, Samuel, Johanna or Frances after their (possible) grandparents?
Jill