My house backs on to a fallow field (which is owned by a farmer), on the border of the field is a tree that overhangs my property. I'm aware that i can cut back anything that overhangs my property, but if it needs doing professionally, should this cost be passed on to the tree owner?
From what I've read in the past, you need to contact the owner about this, and give them the opportunity of sorting it out. Then if you get no joy you can give them notice that unless they do, you will engage someone and expect the money from them. After that, I am not sure, but legally, you are covering yourself.
Also, any cuttings are legally their property, so check whether it would be OK for you to dispose, or if you can't be bothered, put them on their land.