National Army Museum
This large museum traces the history of the British Army, and includes interesting and thought-provoking exhibits that go well beyond a collection of military equipment (though the museum does, of course, boast a large collection of it).

This large museum traces the history of the British Army, and includes interesting and thought-provoking exhibits that go well beyond a collection of military equipment (though the museum does, of course, boast a large collection of it).
Check the official site before travelling; hours and prices can change.
More museums

Sir John Soane's Museum
Free, tiny, deranged — Soane's own house preserved exactly as he left it in 1837.

The Wallace Collection
Free national museum in a Manchester Square townhouse — armour, Boucher, the Laughing Cavalier.

The British Museum
Free, vast, civilisationally heavy — go for one room, not all of them.
Source: wikivoyage