Ok, I live in London, and I have a small garden, with one enourmous tree in
it which blocks off 50% of the sunlight.

I was wondering what I can do about it, I have spoken to the neigbours, they
are quite happy for me to do something as it might improve their light too,
but where do you begin? Can you just chop off a few branches? Or does one
have to get a proper tree surgeon in?

And if so how do I find a good one? Any recommendations (Hammersmith)?