Thanks for all the info everyone.
On William Jay's side I have his parents as John Jay B. 1783 and Elizabeth Moore B. 1782. She married John Salmon on 17th Oct 1802 in Upminster and then John Jay on 12 Oct 1807 in Cranham.
I have her parents as Thomas Moore and Mary Nichols but no dates for either.
It's Eliza Jay's side that's still a bit of a mystery. Like yourselves, I have failed to find a marriage between Edward Jay and Elizabeth ?. From the 1841 census, I have Elizabeth as being born in 1791. If she was a Hicks then there are a few possible baptisms but they are all a long way from Cranham/Romford.
Also, if Eliza was born out of wedlock it might be possible that she was known as Eliza Hicks for a while but then where is that baptism? Everyone was baptised in those days, weren't they?