The British Library (this picture's licence: CC-by-nc-nd-sa).
The new British Library buildings are located near the Saint Pancras station (where the Eurostar trains arrive). Following the main entrance, after the first stairs, panels present the Tapling collection Tapling and some other fine stamps and covers.
In the same hall, a permanent exhibitions of the British Library's treasures is a pleasure for the eyes and the historian: original manuscripts and old drawings, including an history of the Magna Carta. The visit is free, like often in British national institutions and museums, but you are kindly invited to a donation.
I didn't have the time or the occasion to try it, but the Library is reputed to be one of the main philatelic archives and library in the world, alongside the one at the Royal Philatelic Society London. The British Library started by receiving the Earl of Crawford's book collection, that he first donated to the British Museum.
To discover these philatelic archives, you can read the monthly Stamp Magazine. Inside, one page told the story of one of the British Library's interesting items.
So many bookly wealth in this town...
Note 1 : attribute the picture to the author by his name (by), for a no derivative (nd) and non commercial reuse (nc) under the same licence (sa), please.