I believe the main route through London for that sort of air traffic follows the river - it's an easy landmark for the pilots and makes sure they're all taking the same sort of corridor (this info is based on something a helicopter pilot I chatted to once so take it with a pinch of salt).
CiaranMc -Basically you are correct, single engined aircraft are expected to folow the path of the river, thus making "ditching" easier and less dangerous than flying over houses offices etc. Helicopters, whils't most have a single engine have a secondry mode of motion - IE by feathering the blades they can continue on a sort of controlled descent (something like the old gyrocopeters in the 20'' & 30's)
Has any noticed an increase in the number of helicopters buzzing around again? It's like a live encyclopedia of helicopters - there have been at least 5 different types today including the ever present chinooks. There was a weird episode yesterday with a helicopter chasing a plane - it looked like some sort of film stunt. Anyone with a helicopter fetish must be in permanent ecstasy.