Somewhat unrelated: I'm hoping to go to Bletchley Park this summer, any recommendations?
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Whether something is the first computer is - inevitably - a definitional argument, but TNMOC has several candidates (though not all of them) including (a modern reproduction of, the original was destroyed as a secret) Colossus which is famous because of its involvement in the war.
Bletchley Park is also still an actual stateley home, all the war stuff was built on somebody's grounds - there's a good chance you either don't care about stately homes or you're intending to visit a more interesting one (or indeed one of the Royal Palaces), in which case no need to care, but that's a third distinct thing on the same site.
[Edited to make clear there is no original Colossus, we destroyed it because it was a secret]
Operationally independent, although they have been considerate enough to synchronise their opening hours.
If you're interested in London Buses however, I'd actually recommend the (also unrelated) London Transport Museum, as this one is located in the tourist heart of central London in Covent Garden.
( NB: Brooklands is itself a great museum, but more for the aviation history )