This is criminal damage and I would be concerned that his behaviour might escalate if he is permitted to just continue doing as he pleases - how long before he decides a tree is blocking some of his light and has to be cut down, or he doesn't like things in people's gardens etc. Normal people would talk to a neighbour first, open a discussion, ask if work could be done and give their reasons for the request. It is possible that having recently moved in he genuinely thought he was doing a favour for one of his new neighbours. But, he has gone about it in totally the wrong way and personally I'd be worried as well as furious. Oh, and it is unreasonable of anyone thinking it's OK to walk 5 abreast on the path (bloke and his 4 sons you mentioned) - then nobody else, especially people with mobility scooters or pushing buggies, would be able to get past them.
Neighbours are permitted to trim back branches etc that overhang their properties but you say this guy lives up the road a bit so I presume he is not your next-door neighbour and this would not then be applicable. My better half is a tree surgeon and often has to deal with neighbours in dispute about trees and hedges. Mostly even when neighbours want to trim overhanging tree branches or hedges they still approach the neighbour the offending plant life belongs to, either asking them to deal with it or by requesting permission to trim their side, sometimes offering to pay or go halves etc. To the best of my knowledge nobody has a right to just walk down their road with a hedge trimmer and cut their neighbours bushes.
One of our new (problem) neighbours recently butchered a lovely tree - I'm livid, especially as the tree belongs to the nicest neighbour we have (we've lived next door for nearly 30 years and consider her as good as family). Her tree does overhang our garden a bit but she takes good care of it and we don't mind - we know we'd only have to ask or offer to trim it if it ever became a problem (it's a nice tree and the only one of its kind in our gardens). The neighbour mistakenly thought that part of the garden belonged to the flat they rent and wanted their kid to play there (it is OUR garden area and we don't want any more nuisance than they already make right outside our window)
If I were you I'd prefer not to get off on a bad heading with new neighbours but 'd be very concerned and would probably report the incident in case this unreasonable behaviour establishes a pattern. If the trimmed hedge is not a 'neat job' and has damaged it, made it look really bad, disturbed nests etc he obviously doesn't care about the impact on you, your garden, the wildlife etc. I've just re-read your post as I was going to suggest talking to him but you mention an exchange you had with him where he was 'defensive and aggressive' - worrying traits and a bad response. Please be careful as it doesn't sound like he is prepared to listen to reason, obviously has an entitles attitude to do as he pleases, act impulsively and not care about the consequences.