Sleap has a small museum.
I believe Wellesbourne has...something - maybe just the odd aircraft or two though, not sure.
Bruntingthorpe doesn't call itself a museum, but has some amazing aircraft, and is great fun to fly into.
I think helicopters can fly into the Helicopter Museum at Weston-super-Mare, but I don't think there's room for anything needing a runway, not sure.
I think there are more; I'll let you know if I remember any.