Well, elements like The Stig, Star in a Reasonably Priced Car, the Cool Wall, etc., could pose issues.
Years ago when Letterman changed networks the one he left claimed ownership of the Top Ten list, and it was quite a tussle.
Reports are that Chris Evans is lined up to be the main presenter on BBC's continuation, although there's a bunch of confusion and conflicting reports.
I saw him when he was on Star in a Reasonably Priced Car. He was funny, but I don't think he has the kind of personality to carry a show like Top Gear.