This might be Charles?
Red Lion Lane, Farnham, Hants 1851
Richard Williams 48 Cattle Dealer b. Andover
Harriett Williams 49
B. Williams son 20 Cattle Dealer b. Andover
Ann Williams daughter 19 Lace Bonnet Maker b. Andover
Charles Williams son 16 (looks like) sl or fl house b.Andover
Hannah Williams dtr 12 (looks like) sl or fl house b.Andover
John Williams son 11 servant frm b.Andover
William Williams son 6 Scholar b. Andover
This is the only other reference for a Charles Williams b.circa 1830 at Andover. However there are quite a few Charles Williams who only list their place of birth as in the county of Hampshire, so this "evidence" remains circumstantial in my book at the moment.