Not knowing the area, I looked it up on Multimap and it looks like Cavendish square is almost a mile from the parks you mention. While that is not far for a gentle walk, it leaves your average paramedic, doctor (and pilot) gasping a bit when they have to run with kit. Life becomes even more interesting if you have to carry the patient back!
From what you say, it sounds like resources on the ground asked for the aircraft to land at Cavendish Square and cleared the area for it's arrival. I suspect that the square was assessed as the most appropriate landing site for the incident location and the Pilot then has the ultimate decision as to whether it is safe.
There really would not be a logical reason to turn down the landing site on the basis of it being "one of the windiest parts of London" and "trees and buildings metres away from the rotors" is generally speaking, par for the course.
Cheers
TeeS