Tree in a neighbouring garden
A tree in a garden, or other private land, is the responsibility of the owner. If a tree in a neighbouring property is causing you problems, take it up with your neighbour or the property owner.
You have a legal right to remove branches that cross over your boundary. But you can only do this from your own property. You must get your neighbour's permission to cross the boundary - even to lean a ladder against the tree trunk.
Don't put the branches on your neighbour's land. Ask your neighbour if they want them: it's your responsibility to remove them.