Reading this I get the feeling that there is a lot of doubt as to what the law actually says on this point.
So I suggest that OP checks that first.
Then, depending on how willing she is to risk offending her neighbour, she can either refuse to pay for the removal of the cuttings, and risk a feud with him, pay the amount he is demanding, or pay less.
It might be as well to pay this time, if he is legally entitled to demand payment, but to tell him that in future, you would prefer him to tell you in advance when he intends to trim the hedge.
I think, I would ask him whether he would consider suggesting what height he would like it to be, then cut it down to that height.