Sure, plenty of people can wander round inside the base - once inside (thought last time I did that at Colt, with the chap giving me a tour round the interesting bits, we were stopped 5 times to ask us what we were doing).
But walking up to the guard room and saying 'just popping in to see the museum' will get you NOWHERE.
Yeovilton's museum is not part of the base. Coningsby's BoB museum thing is not part of the base. Neatishead's museum has closed. Dunno about Uxbridge but as I say, you can't get in without prior arrangement where such facilities exist, and you'd have an escort at all times.