Hello, we have a big maple tree in the street outside our house in Honor Oak, which has been 'pollarded' - technical term for 'cut back' - in the past, and is in need of it again. I, like you would rather not lose the tree - even though we have had some issues with subsidence, but I called the council last week (Environmental Services) and although the person I spoke to on the phone was not the most helpful or friendly, I did receive a call the next day from a very helpful man, who said that the tree was already on their radar and they would be attending to it in the near future after all the priority 1 trees had been dealt with, ie the ones that have health & safety issues.
Hope that helps!