Speaking from experience here, and this is English law only.
If your neighbours genuinely thought that it was their tree/bush (even if it turn out that they were wrong) it’s not a crime, they would have needed to deliberately damage someone else’s property knowing that it’s not theirs for it to be criminal damage. Even if this is the case, the police will not care.
It’s a bush.
They’ll give you a crime number and will probably close the case as a non-crime - makes the stats look better.
Using your crime number you can speak to your insurers if you have legal cover and ask them to get involved but for the sake of a bush worth a few hundred pounds at most they won’t care either and your excess will probably be more than the bush is worth.
Sadly you’re left with little recourse unless you want to fund a legal case yourself but for something so small there’s little point - it’s a civil dispute and the court won’t be interested.
This sucks but that’s how things are.
Talk to your neighbour first, ask them to do something about it if you want, maybe even pay for a solicitor to send them a letter saying you want a new bush but anything more than that you’re throwing good money after bad