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Personally I’d say let him call the police, he’d need to provide proof that you damaged the wall deliberately! Storm damage is considered an act of god and therefore no one is held responsible, though he should have maintained the wall & kept it in a good condition. I’m not sure about conservation areas but generally a landowner does not have to rebuild/replace a boundary wall/fence. That may well be the same in a conservation area if the wall doesn’t have a protection order on it or if it’s not listed.
I would speak to your local council and also get legal advice from your insurer, most household insurance policies have additional legal cover. However, it’s likely to be a long drawn out issue, and your not so nice neighbour may become even more difficult! Maybe worth considering just putting up a wall/fence/hedge within your own garden