I can't see an entry for a Charlotte Fulwood in Hitchin on either the IGI or Ancestral File. Later Found it on the Pedigree Resource File. Birth in Hitchin, baptised in Southill. It smells. Thomas is shown as born in Hitchin, married in Warwick, then back to Southill. Iffy! As there are no birth records pre 1837, just baptisms, there's no way to confirm the alleged birth.
There is a baptism in Southill on 15 May 1766, daughter of Thomas and Sarah, shoemaker. There's also a baptism of Charles Fulwood in Southill on 3 Jan 1769 son of Thomas and Sarah, shoemaker. On 3 June 1768 there's a baptism of Decima Fulwood daughter of Thomas & Charlotte, husbandman, which I wonder about. Was the mother really Charlotte or is the PR in error? I suspect it is
There are no Fulwood marriages or burials in Southill
Thomas and Sarah Fulwood baptised four daughters in Hitchin from 1771 to 1776 - Lyddy, Sarah, Sophia and Desimus. I don't have burials for Hitchin for that time but it would be interesting to see if Decima baptised in Southill was buried there.
It looks to me like the same family - Hitchin is only 10 miles from Southill. You need to post on the Herts board to get details of the Hitchin baptisms to see if Thomas was a shoemaker.
David