Were the branches all overhanging his property?
The neighbour is only permitted to cut overhanging branches on his side and only so long as this does not harm the trees.
He is therefore going to be liable to you for damages.
The damages are equal to what it will cost to put you back in the same position you would be in had he not done this.
This is also trespass though the police will most likely say that this is a civil matter.
I suggest you consult with a lawyer with a view to retaining the lawyer to send him a demand letter requiring him to compensate you for the damages.
I also suggest you call a tree specialist to tell you if the trees will die, how much it will cost to replace them etc.
You can contact the Law Society and use their Lawyer Referral Service. You will be given the name of a lawyer and can consult with the lawyer and the first half hour will be free.
Here is the contact information you will need.