If this had is indeed shared, then she has as much right for it to be removed as you have for it to stay. If this were to go to court, and it was agreed that the hedge was on the boundary, the court will normally maintain the status quo which means they would leave the hedge as it is.
If this Becomes a full-blown argument,then you are going to need some evidence from the boundary surveyor as to which side of the boundary, in the surveyor’s opinion, the hedge is on. That may be inconclusive. A boundary surveyor’s report is likely to cost about £600 plus VAT.
If you think the neighbour is going to remove the hedge one day when you are at the shops or on holiday, then you need to get an injunction to stop that happening. If there is some urgency with this because you think the neighbours about to do it in the next couple of days, you can make an emergency application to court for an injunction to stop the hedge being ripped out pending the resolution of the boundary issue and ownership of the hedge.
Check your house insurance to see if you have legal expenses cover that would pay for the legal costs of dealing with this. I can tell you now, that I have dealt with one of these before and even without getting to litigation the client spent almost £4000 in legal costs. In our particular case, there was actually a known old chain-link fence in the hedge on one side and it was obvious to anyone who owned the hedge but the neighbour wasn’t having any of it. In the end, the neighbour saw sense and moved but it was quite a protracted argument.
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