MJB : Battersea serves one small part of London. It would hardly be your "go to" destination if you were more than a mile from it - given the safe alt we have available for an auto (worst case scenario).
We've already had instances of people putting down elsewhere in London - there is no rule that prevents you from being safe.
In any case, even Heathrow accepts precautionary landings with no charge. They ask you to use a heli aiming point, then a vehicle escorts your air taxi to a place of safety. Spent a very nice 15 mins in the cargo area with a precautionary check a few years ago. No charges.
I'm sure Battersea would do the same.