Elizabeth, all my sympathies. It's a nightmare situation and so many differing rights and wrongs.
Just been looking for further info as I have the same problem with my neighbours. I have also had problems with the Council over telephone wires dragged down by their trees. They are not interested and blame BT, they say it's the Council as it's across the main road. So on and so forth.
Private properties (neighbours) and ruling for Council property seem to differ. Also I have read that the practice of topping trees is now a 'no go' area for Council property. It can cause disease and there's all sorts of other reasons. They do not cut trees because it restricts light. So basically I would imagine that your friendly Council are unlikely to respond and it looks as if we are quite likely to be living in a forest again soon. My neighbours garden is already a forest, 10 years since anyone touched it and still counting. It includes amongst others about 3 holly trees well over 25ft tall, and holly wood is very hard and the thicker it gets the harder it is.
Horrendous now and making my job ten times worse. No longer is it possible to reach even the lowest branches of the trees and therefore, the same could happen to you. Think about it