It's a members-only library but you might be granted access with a research request. The writer's room is great but there's a few special, hidden corners among the bookshelves to tuck yourself away in.

Lovely pub/cafe. Great atmosphere, best to sits outside 

A treasure trove in the The City of London. The Archive of London. Strongrooms hold kilometres of shelving; boxes of matter that has somehow been catalogued and categorised in a traceable manner by the public, for academic, genealogical and other research. This beautiful book is from a box on Epping Forest. On the same visit, I looked through photographs of Blitz singsongs in Bethnal Green Underground station, 1980s anti-Thatcher / pro-GLC gig posters and paper concertina optical models of the Crystal Palace.

Outside of the major players (Tate, V&A, RA) this is probably the best programmed gallery in London

On Burlington Gardens in Mayfair, Cecconi’s is a modern-day classic Italian restaurant open for breakfast, lunch and dinner, seven days a week. Cecconi’s serves handmade pasta, seafood and dishes from Italy using the finest ingredients. The restaurant has outposts in West Hollywood, Miami, Istanbul, Berlin, Barcelona, New York, and Mumbai.