Legally, your neighbour does not have to cut them back. Only if they were causing physical damage to your property, could you sue them and demand that this action is taken.
However, you are permitted to cut back the branches yourself, up to the boundary line. You are then under a duty to pass the cut branches back to your neighbour- either by handing them back to them, or placing them back over the fence.
The above assumes that there is no Tree Preservation Order on the tree- if there is, you would need the Council's consent before you touch the tree.
I hope this assists and sets out the legal position.
Hi, can I assist any further? If not, I would be grateful if you could rate my answer. Thanks Al