Just walking around London will tire you out. If you're getting the tube, walk up the left hand side of the escalators rather than standing on the right. Check out all of London's Royal Parks, just walking from one side of Hyde Park to the other will give you a good work out. Cycling in London is easy thanks to the bike hire scheme but do make sure you know to stop at a red light etc. nothing more annoying for Londoners than tourists running into pedestrians because they don't know they need to follow the traffic lights. Go Ice skating in Streatham. Most local areas (outside central London) have local swimming pools depending on where you are staying. Get to Crystal Palace and walk around the lake and see the dinosaurs.
Oasis swimming pool, heart of West End http://www.better.org.uk/leisure/oasis-s...
Running in the parks (Hyde Park, Regents Park, Green Park etc etc)
- hire a Boris bike
- go for a run; lots of parks!
- open air swimming pools / lidos
- pay as you gym
- free 3-day membership of LA Fitness gyms
- find a class (yoga, Pilates etc)
the "boris" bike rentals are all over central London
http://www.tfl.gov.uk/modes/cycling/barc...