Your William Cook was, according to census, bc.1796 Englefield, Berkshire. He was actually a couple of years out:
William Cook bp.11/2/1798 Englefield, Berkshire, son of William and Amelia
at least 3 siblings:
Elizabeth bp.23/3/1800
James bp.1801 (full date not shown)
Richard bp.10/7/1803
William Cook married Amelia Wise 9/7/1797 Sulhampstead Banister, Berks.
(Sulhampstead just SE of Englefield).
Annette