In the UK you have the legal right to cut back any branches of a tree which overhangs your garden. However, in legal terms, the branches which you cut down actually still belong to your neighbour (although s/he is unlikely to want them back).
In terms of neighbourliness it is advisable to have a word with your neighbour before you cut back the branches, just so that they are aware of your plans and if they object you may be able to resolve this by negotiation (although lawfully you are in the right).
You do need to be careful when actually cutting back the branches. If you cut off any which are actually on his land then he could accuse you of damage to his property. If this concerns you, it may be prudent to have a tree surgeon in, but you would have to bear the cost of this. Not your neighbour.
In terms of neighbourliness it is advisable to have a word with your neighbour before you cut back the branches, just so that they are aware of your plans and if they object you may be able to resolve this by negotiation (although lawfully you are in the right).
You do need to be careful when actually cutting back the branches. If you cut off any which are actually on his land then he could accuse you of damage to his property. If this concerns you, it may be prudent to have a tree surgeon in, but you would have to bear the cost of this. Not your neighbour.
