As Scott says, you will need an EA licence for freshwater fishing - Saltwater is still free to all. Once you have that, you will however still have to pay to fish most waters.
You can order the EA licence on line but make sure you keep details of the number etc as even if you don't have the physical licence, the balifs should be able to confirm that you have one by checking the database.
Best advice I can give is to sign up to a UK based angling forum such as AnglersNet (link below) and post up details of exactly where you'll be staying, what kind of angling you're intereested in and when you'll be over. I'm sure that some of the members who live close to London will be happy to help out.
http://www.anglersnet.co.uk/forums/Coar ... bccf8c2ca4