Go to the Museum of London, it's near St. Paul's Cathedral and it's free.
National Express takes you from the Stensted Airport to the Victoria station in the city if London.
Duration: 2 hours
£ 18 Return ticket if you buy it in advance online.
Tube in London: make sure, you have your oyster card (you can buy it in Germany) and don't forget to register on their website. The Busses don't take cash anymore and the tube is not that difficult to manage!