Rick's and others' guidance on this forum describe many terrific places to visit. I wanted to share one that I found highly engaging, but out of the standard American tourist stop. If you are interested in military planes, the RAF or the Battle of Britain, Tangmere Military Aviation Museum should be considered very, very much. It's free, but they do ask for donations.
Find out about the place at https://www.tangmere-museum.org.uk/about-tangmere...
They have one of every fixed wing plane that was assigned to this now-decommissioned RAF base. They offer "rides" in simulators. The docents are highly knowledge, extremely friendly, and excited about the information they share.
Practically next door is St. Andrew's Church. In the graveyard is buried the first American killed in the war; he was serving in the RAF prior to the US entry, and he was and RAF pilot who was killed during the Battle of Britain.
It's in Tangmere, Chichester, UK. We were visiting friends nearby, so got there by car. I'm not sure how accessible the location is by public transportation -- especially from London.
Also nearby is Goodwood Aerodrome. If you're flush with extra travel funds, you can catch a ride in a Spitfire. If you're not flush, you can watch the Spitfires come and go, depending on their passenger list... Both are very impressive.