Who has told you that the neighbour does not have to make any contribution towards cutting back the tree?
Please confirm that the tree is not subject to any Tree Preservation Order.
When you say felling the tree, you mean trimming it back or getting rid of it altogether?
If you could explain the situation in detail that would be helpful please.
It’s essential that before doing any work on a tree on which there is a Tree Preservation Order, the person wishing to do the work gets consent from the local authority. Evergreen trees are rarely subject to Tree Preservation Orders if they are on private land.
Any branches which overhang the boundary are trespassing. You can either cut the branches off yourself and let the neighbour have the branches back. If you keep them, he can claim that you’ve stolen them. He may not be happy if you simply throw them over the hedge into his land so ask what he wants to do with the pieces you remove.
If you don’t want to do the work yourself which is going to be the quickest way of dealing with this, you can go to court to make him abate the trespass and remove the branches and pick up the cost of doing so. There is always a cost risk with litigation and this could easily take several months to get to court. There is no guarantee that you would win. It’s likely that you would but litigation is never guaranteed.
You could get someone else to do the work and then recover the money from him. If he doesn’t pay, which seems likely, you would have to take him to the Small Claims Court.
Whatever you are going to do you need to write to him to say that unless he agrees a course of action within the next 21 days (it needs to be a reasonable period) you will take the course of action you think appropriate.
Can I clarify anything for you?
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That’s reasonable. Make sure that you tell him exactly what the deadline is and what the cost is. That way, he cannot say that you never gave him the opportunity to do the work himself which no doubt he will claim he would have done for a tiny percentage of whatever it cost you. Make sure that you keep a copy of the letter.