I understand that you can cut back any parts of vegitation that overhang your land. However, they are not your property and you must return then to the neighbor.

He is not obliged to cut back if he sees no need.

How about contacting your local council and asking them what the regulations are.

Just a thought - tree preservation order may be in place?

Would also reitterate speak to a lawyer if you think things may get out of had. Is there a local tree surgeon who may give out advice - they'd be bound to have been in similar situations.

Good luck