.co.uk or .com makes little difference apart fom what people expect it to be. I imagine .co.uk makes more sense due to it being a UK show.

Perhaps what's more confusing is the having both a domain and a name for the archive. So whilst primevalarchive.co.uk can work as a domain then there's still the matter of the archive name, on which I think I rather like The ARC but shall have to see what the end of the season brings re that.