I don't know the details of the incident you were witness to, but some background on the HEMS operation might help.
They are called only after some pretty tight screening at the 999 center in London, and dispatch with a doctor on board.
They are able to land within 100 yards of the site of the site in order to make the transfer to the helicopter as quickly as possible. The doctor makes the decision whether to transport the patient by helicopter or ambulance and to which hospital - the ambulance folks don't have nearly as much training or experience as the doctor, which is why the helicopter is so valuable.
And they land in a lot of places where the clearances are tight, probably tighter than Cavendish Square...