Hmm, well, let's answer this in two parts - the laurels belong to your neighbour, and its your neighbour's choice whether or not they let them grow, have them cut, remove them, or spray them gold, its up to them what they do with them. If they're hanging over your boundary line, then you can trim them back to your boundary line (imagine a vertical line from the top of your fence or wall upwards), but you are not allowed to remove any more than that, and the cuttings so removed belong to your neighbour.

Aye, cut them back and throw the cuttings back over the fence :)

As you have to live next door to these people, I suggest you ask them if they want the cuttings back rather than just chuck them over, lol!