"such a dangerous landing" It's not dangerous to land Cavendish Square.
I've never noticed it's "one of the windiest parts of London" but, even if it was windy, I can't imagine the wind being outside safe operating limits. In the unlikely event that it was, the pilot wouldn't have landed.
"trees and buildings metres away from the rotors? There are some trees in the Square (not many) but buildings metres away??
"Hyde park, Green park etc which are only a stones throw away and would be much easier and safer to land in?" A stone's throw away? Are we talking about the same Cavendish Square? Behind John Lewis department store? A suitable landing site in Hyde Park would be about a mile away. If there is a suitable landing site in Green Park, that's the best part of a mile away. I assume the air ambulance was used because it was an emergency - not much point in landing further away than necessary.
One of the great things about helicopters is that they can land virtually anywhere, and in a very small space. From your description, it seems things on the ground were handled efficiently to ensure the helicopter could land safely.
I'm not surprised you were impressed by the flying. Pilots who fly for the emergency services are skilled and experienced.
If it happens regularly, Cavendish Square sounds like a good place to have lunch.

I've never been lucky enough to see it, but I understand the London air ambulance lands at Picadilly Circus when circumstances demand.