The Lee Valley White Water Centre was originally opened for the London 2012 Olympic Games to host canoe slalom events. Today it's the only place in London where you can go white water rafting (ok so it's in Waltham Cross, but that's only 50 minutes away from Liverpool Street Station).
The venue has suitably intimidating/ thrilling rapids so you'll feel as close to the real thing as possible. More gentle activities like kayaking are on offer too.