Posted: 22/05/2015 at 23:50
I don't think it's worth falling out with your neighbours over this as your hedge will recover. Just have a quiet word about respecting your boundaries and property and discussing any perceived problems and never taking unlateral action.
I think you should check the height of your remaining hedge and maybe trim what's left to the 2m height now accepted as the maximum acceptable height for a hedge. That will make the new gap less obvious.
I also think that if you feed it, your hedge will grow back more quickly than any new climber could to fill the gap so by next winter or maybe early next summer, it can be expected to have recovered. I would suggest a generous dollop of blood, fish and bone or pelletted chicken manure at the base, just sprinkled about and mixed in lightly with a fork or hoe. If you also give it a spray of liquid seaweed feed or similar all over the foliage it should put on some rapid regrowth.