It's highly unlikely they will want to move the fence now it's up. Why don't you call around and thank them for putting the fence up and tell them you intend chopping down the trees, they obviously didn't like them.Most neighbour ask for half the costs so you are very lucky. The boundary line will be registered in the deeds of your house and the Land Registry so unless this crops up when either of you sell there shouldn't be a problem. A good site to try regarding boundary problems is the forum on www.gardenlaw.co.uk. Life is too short to argue over a few feet of garden, it once cost my brother �6,000 in a court case over a 14" strip of land on the boundary. Bonkers!!