Hello, I am a solicitor with 20 years experience. I will try to answer this for you.
He had absolutely no right to do this. He had the right to chop down the overhanging branches, but not to come on to your land and cut down the trees.
Do you accept that the trees were dangerous at all? Had there been any complaints about or discussion regarding the trees?
He has committed the crime of criminal damage and you could bring the police into this. If he is prosecuted you could end up with some (but probably insufficient) compensation.
He has trespassed on your land and damaged your property. if there is quantifiable loss to you (eg the cost of replanting the trees etc., the loss of the value of the wood in the trees) then you could bring an action in the civil courts, probably as a small claim.
This link will tell you how to do this. https://www.gov.uk/make-money-claim-online
Whether you take action or not is a judgement call for you and depends upon whether you want to see justice done or whether you want to try and preserve any sort of relationship with your neighbour.