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.
Cordings situated in piccadilly is a renowned establishment for British Country clothing and tailoring - that can not only kit you out to shoot pheasant in the finest yellow ochre cords but for me offers a great selection of socks.
The Wellcome Collection is a free museum and library, mostly dealing with medecine and social history. The exhibitions are unusual and engaging, and the permanent collection includes bizarre items such as medieval masks and human remains.