A couple more suggestions:
There's a rather good little museum at Coventry Airport (Baginton). In the summer, when there are plenty of volunteers, you're allowed to sit in the cockpits (Starfighter, Phantom, Lightnings, Vulcan etc). As well as the jets there are exhibits from the days when Armstrong Whitworth had their factory on the other side of the airfield. Well worth a visit. Also Air Atlantique have their Historic Flight based at the airport.
The second suggestion is the Newark Air Museum, a couple of miles east of the A1. There's gliding alongside the museum, and the runway was long enough to fly in their Vulcan - which must have been some sight! Mostly early jets, but some WWII memorabilia.