Overgrown and dangerous tree in neighbour's garden

I wondered whether anyone had any experience of dealing with a helpful Harringay Council person (or other local official) re matters similar to the above. There is a beautiful but huge tree in our neighbours' garden two doors down which blocks out light, has caused some structural damage and is dangerously tall, not to mention the leaves that have blocked our gutters and caused problems with damp etc...The main issue is the property in question is rented and the owner is in prison due to a vast array of misdemeanours including illegal house conversions into flats (such as the house in question) and stealing electricity etc. The Council say that because there is not a preservation order on the tree they have no powers to do anything and have suggested that we put a note through the door! This is despite the Noel Park Estate being a Conservation Area. Ourselves and some of the neighbours are willing to pay to have some of the height chopped down (while the tree has no leaves on it) but without permission from the landlord we can't really access his garden as we'd be tresspassing and I don't fancy upsetting the him!! We've spoken to the Noel Park councillor who suggested we send a petition to Harringay Council but I'm not conviced they'd act on this. We just don't know who to try and speak to next. Any suggestions very gratefully received. Hx