I just picked up your message (2001?) and I can possibly add to your knowledge. I have Eliza bap.2 May 1814 St.Michael's Church, Coventry. One of 6 children.
Parents William Alcot or Allcot bap.5 May 1789 same church, stonemason who married 1 Mar 1813 same church to Mary Everard of Ryton-on-Dunsmore, near Coventry. One of 5 children. William was a voter at Rugby 1832 although a resident of Coventry. You will know that they later moved to Rugby.
Grandparents of Eliza = John Allcot or Allcott, stonemason of Coventry and Ann Elizabeth. No more details.
One Alcott produced what is described in one publication as a "charming coloured marble chimney piece with ogee arch in School/Chaplain's Room at Arbury Hall, Nuneaton. Possibly the finest example in England of early Gothic revival". The Hall was built 1750-1790.
I am not aware that I am related to your ancestors, as I have been stuck for many years at about 1750 at Middleton, North Warwickshire.
Please let me know if you want the details I have of the other children mentioned above.