Don't forget that in London there is also
Falcon Heliport (previously known as Vanguard). The other side of London from Battersea (or
London Heliport), also on the Thames, and closer to Canary Warf and the City. I have been in / out Battersea several times, but not Falcon (only over-flown it) so can't speak practically about the approach / departure profile. However, they do seem to me to be "more interesting," as Falcon doesn't have the landing pad extended into the river like Battersea.
Pictures on the site linked.