A thorny one to which I cannot offer an answer.
However... perhaps the Citizens' Advice Bureau can offer advice - or recommend a solicitor that can offer advice cheaply.
It is an advantage that you do get on with your neighbour - and I imagine he would not wish to cause you distress. Has he talked to the council as they own the property?
If all else fails, could you go shares and get a tree surgeon to look at it and see if the problem root(s) can be killed off or removed?