I am going to suggest putting the City Mapper App on your phone. This is an invaluable tool in London as it gives live maps and transit suggestions. It knows your current location (with your permission) and you simply type in where you want to go. It will give you options, tell you how long the journey would take, and give you a map that shows you how to walk to the nearest bus or tube stop. Once on the bus it counts how many stops you need to go and notifies you when it is time to get off.
I have used City Mapper in several cities (including here in Seattle) and I found it extremely useful in London.