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.
In terms of materials and form, these galleries offer so much. On an abstract and typographic level, so useful. This is a section of an altar frieze, from the Eye Temple at Tell Brak (N.E. Syria), dated 3300–3000BC. The Egyptian rooms take the tourist weight; these spaces are much quieter and amenable time spent drawing and thinking.
Not the most exciting place inside, but a lovely rooftop area which not all that many people seem to know about, 2 mins walk from Old St station. If it's packed then The Red Lion is just up the road.