Thank you for your question
My name is ***** ***** I shall do my best to help you.
It is bad news I am afraid - you have no right to cut the branches back UNLESS they are actually coming over onto your land.
Your only option is to try and discuss the issue with your neighbours and hope that they will agree
Please ask if you need further details
If the height is above 30cms at any point then yes you do
legally of course you should apply - and I can only give you the legal position