speak to them and say it is their tree spanning form their property, they must pay for upkeep of their tree on your side ie errecting fence etc
you are well within your rights to saw through the tree on your side,
write them a letter and send a copy to your local council saying it is ruining the view of your garden ensure you make your intentions clear ie 28 days to errect a proper fence or you will have no alternative to cut the half on your side of the boundry and exert preassure on the tree from your side to make it fall to their garden as it is their tree,
ensure you make a cc note on the letter to say you have sent it to council etc
if not find a vandal give him a can of petrol and matches, and usually a bottle of vodka
hope it helps