Hi Nigel.
This is undoubtedly the marriage of the parents of that William you found on the IGI William
Clarke Birch 17/11/1816. From the Sussex Marriage Index;
Arundel, West Sussex, 30 Dec 1807:
William BURCH, bach
Mary CLARKE, sp botp
Four daughters are also listed to them between 1808 & 1821 in Arundel.
Does your William say where he was born on the census?
I'm rather skeptical that these two are the same William. This William was obviously around in 1821 fathering children so it's not as though he died when this William was an infant, therefore not known to him and he bears the same name. Also this William takes his mother's maiden name as a middle name but doesn't use it on his marriage certificate. What about witnesses on the certificate, sometimes they give a clue, also the names of the children he had with Ann can also point you in the right direction. Have you found him on other census's?
Loads of questions,l I know but they might get you thinking

jane