There was an article in either "Pilot" or "Flyer" magazine a few year's ago about single-engine helicopter routes across London. Now, if I remember the article correctly, pilots using these routes were expected to land in the Thames in the event of engine failure. I have always assumed (perhaps incorrectly) that the same option was available to single-engine aircraft.
Don't forget to take the wind into account.
One point that I don't think has been mentioned is that the landing fees are higher at Biggin than at the North London airfields, but you will save significantly on the flight time by using Biggin, and as has already been pointed out, you can expect to be treated in a professional manner.