Posted: 20/01/2015 at 09:01
If the main trunks are in the neighbour's garden you are entitled to cut right back to the boundary and you are required to offer the cut branches to the owner. Allowing the branches to remain over 1.5 metres will look distinctly odd and realistically it is a case of cutting back the whole height or nothing. It will look dead and unsightly on your side, though the neighbour's side should continue to grow as normal.
Do try to discuss the matter with your neighbour before going ahead as war could break out. Invite them in for a coffee and to see the problem from your side. Have alternative solutions to offer (eg. Sharing the cost of a new hedge)
These trees are a nightmare. There is legislation in force but it is pretty expensive to lodge a complaint with the council. Best all round to try to come to an amicable agreement. Good luck.