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.
A short walk from Oxford Circus tube station, Kaffeine is easily one of the best coffee houses in London. Whenever I'm working in the area I pop in beforehand to kick start my day with a well-made cappuccino.