You certainly/clearly replied to me… 
the original poster has found the answer to her query… and is looking forward to a blossoming friendship with her neighbours… 
Interesting, I’m pretty sure I checked with a reliable source - though you can’t really sniff at the advice on the official government website.
OK, maybe you can’t cut them yourself but:
You can require that your neighbour cut them.
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legally I understand that they should ask you first to do it. I think that trespass is illegal. Good luck we are having problems with our neighbours in spite of the mayor saying they should ask us,
thought that the hedge was not theirs.
I believe that if the plants/ bushes grow to over 2 metres they should be planted 2 metres from the boundary with your neighbour
HI Hugh and welcome to the forum.
If you read the entire thread… you will see that there have been misunderstandings… now resolved… and Harriet is now becoming good friends with her neighbours…
Re your own situation… the boundary dispute (more or less any dispute) between neighbours is not really something for the Maire to sort out… although, or course, he will be keen to encourage folk to be good neighbours… and to do “the right thing”.
If you feel your neighbour has acted badly… you can send them a recorded delivery letter, asking them to put things right/stop what they are doing/ whatever… with the threat of taking them to court if they persist. This route is for you, not the Mairie. Often the Mairie will try and talk to both sides… to mediate/ help ease tensions… but it is not really part of their remit to dictate on neighbourly squabbles…