The first thing you should do is have a conversation with your neighbour to see if you can agree on a schedule of work for the tree or hedge. If you are unable to agree, then you usually have the legal right to prune back anything encroaching over the boundary of your property. Please bear in mind; you must still check for Conservation Areas and TPOs.
Unfortunately, if the height is the issue, you have no legal right to reduce them. You may be able to get the tree removed if it poses a risk to you or your property, but we must still apply for immediate permission from the council under an exemption for dead or dangerous trees.