I'm struggling to make sense of what's where and in what order so I'll give you the general lowdown until there is more clarity.
If you have trimmed foliage/branches/bushes/whatever that is overhanging onto YOUR property you are allowed to do this even if what you have trimmed actually belongs to someone else (i.e planted in a neighbours garden.
If you have trimmed further than that or to the extent that the "hedge" no longer forms such you could well find your self in hot water. You do state that this is not the case, but in some posts it sounds like it might in fact be the case.
I wouldn't go down the road of escalating to landlords or other bodies if you can avoid it.
Something similar, but far more severe happened to me when my neighbour absolutely fucking MASSACRED MY hedge. After going completely nuclear at him I sought legal advice as he entirely destroyed the hedge and my privacy in the process.
Interesting little nugget - I successfully sued the shit out of him. He tried to argue that he believed the hedge was his, or at the very least "shared" - not so. Ownership is decided ENTIRELY by whose land the hedge/tree/whatever is actually planted on and nothing else. It matters not what the deeds show either, although this won't usually be an issue unless boundaries are vague.
If said holly trees are planted in his garden, they are his (provided he hasn't nicked the land they're on to claim as his own)
If said holly trees are planted in the alley, they belong to whoever owns said alley. In either case you can trim what overhangs your property provided you don't butcher it in such a way as the "plant" is severely damaged or killed off. Snot allowed.
That's the legal position, I spent a hell of a lot of time researching this when it happened to me last summer, my solicitor massacred him in the same way he massacred my hedge.
HTH