The best thing about any charity shop is that you never know what you are going to find. I have a well tested route around London that includes all of my favourite charity shops. This Oxfam has a great selection of books and often turns up some interesting clothes too.
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.