Is it illegal to cut back our hedge?

Just moved in and inherited a very overgrown garden. Roughly 5-6 feet of our neighbour’s hedge was encroaching on our path, so we decided to take it back so we can install a fence and plant some plants, trees and flowers to enjoy on the walk up to our house.

I met the neighbours earlier and they very quickly told us that we shouldn’t have done any of this until September, and we could potentially be in serious trouble for doing so. From what I can tell, this would only be illegal if we KNEW a bird was nesting there in the exact bush and still went ahead with taking it back. Am I right here?

They also mentioned that the bee’s love it (nothing about birds) – however we haven’t seen a single bee in the bush and there’s not a blossom in sight, so not totally sure about that…

On the other side of the garden there’s tons of bees and loads of birds dashing between the bushes in which I assume they are nesting. The side we chose to cut? Nothing. We haven’t seen or found anything yet.

The job isn’t quite done yet and we’re getting pretty paranoid, nervous and also a bit embarrassed that we’ve done something horribly wrong and might even get a knock from the police if next door, or anyone else who can see what we’ve done, chooses to escalate it.

Obviously we will be even more careful in inspecting the areas before we continue, but I was hoping that someone could in the meantime please let me know if we can even carry on or if we need to wait until September!