Lambeth Palace
The palace has been the official residence of the Archbishop of Canterbury since the 13th century. Guided tours of Lambeth Palace are incredibly popular and there has been a substantial waiting list for some years.

The palace has been the official residence of the Archbishop of Canterbury since the 13th century. Guided tours of Lambeth Palace are incredibly popular and there has been a substantial waiting list for some years.
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