I have trees in my garden that have gotten out of hand. The require pruning by a professional tree surgeon, but how do I describe the job in hand when enquiring?

My neighbour's hedge, and a tree within it, are both encroaching into my garden over our boundary fence. Before I take matters into my own hands and have the offending growth cut back, am I safe to instigate this or is it seen as interfering with…

Now that the weather's improving I think I need to have some tree and hedge work done. But with it being late June, have I left it too late?