Not sure if you would make EGLC - and they may have something rolling/short final. There are of course lots of buildings and no room for error of you get it wrong (unless you fly with lifejackets on!)
The reason that I give routings up the Lea Valley is it is generally uncongested. There are a lot of places to let down there aren't there (and a few big expanses to the South of City in Greenwich area)
Failing that, the Thames. Probably a good chance of being rescued from a boat there! I think that you would do well to make LCY.