Well, Battersea get restricted when LCY is on runway 10 as it is (as traffic has to be at 2000ft downwind and on base leg....)
The ATC and City Airport issues will be the hardest thing that I can see. Also, I am sure to do enough movements to make money will mean Air Traffic Controllers needed.
London definitely needs a heliport that is better placed etc. Around the London Eye would be best placed geographically.... but locals and noise and Red Ken are massive obstacles....
Good luck