Household Cavalry Museum
Horse Guards is a historic building in the City of Westminster, London, between Whitehall and Horse Guards Parade. It was built in the mid-18th century, replacing an earlier building, as a barracks and stables for the Household Cavalry. The current and previous buildings were, between the early 18th century and 1858, the main military headquarters for the British Empire. Horse Guards originally formed the entrance to the Palace of Whitehall and later St James's Palace; for that reason it is still ceremonially defended by the King's Life Guard.
Horse Guards is a historic building in the City of Westminster, London, between Whitehall and Horse Guards Parade. It was built in the mid-18th century, replacing an earlier building, as a barracks and stables for the Household Cavalry. The current and previous buildings were, between the early 18th century and 1858, the main military headquarters for the British Empire. Horse Guards originally formed the entrance to the Palace of Whitehall and later St James's Palace; for that reason it is still ceremonially defended by the King's Life Guard.
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