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.
Even if you have seen it hundreds of times it will still stop you in your tracks. A great piece of architecture and apparently the largest brick structure in Europe.
The most special and charming cinema (probably most deprived too) in London. A place to catch a classic or a new release. You can get a lifetime membership for £50, weekly £1 member screenings. A place where staff are as passionate about pictures as its visitors. A must visit for movie buffs.