none if its his plant you can only cut back what overhangs your property and offer the prunings back to him
if it is your plant you can do what you like so long as you don't trespass on his property to do it or do any damage in the process... neighbours cut back a beautiful portuguese laurel that overhung our deck but it was his bush but we really missed it
First you should ask your neighbour to do it. Only if he/she refuses or doesn't respond can you go ahead, and only on reasonable grounds. If there are roots threatening the foundations of your property, or really huge branches cutting your light, or something poisonous, you'd be best advised to go and ask the Citizen's Advice Bureau, as they will know if you really need proper legal advice. You may kill his favourite tree, for instance, so you had better find out where you stand, first