Although this is common law nuisance, you will be better dealing with this under the Protection from Harassment Act.
Harassment is a course of action (more than twice) which is intended to harass, the culprit is reckless as to whether it harasses, does harass, or the average man in the street would think that it was harassment. It doesn’t necessarily have to be intentional.
It’s unlikely that the police will prosecute purely because of the lack of evidence to prove harassment, beyond all reasonable doubt. However, by all means complain to the police but before doing that, make sure that you have the dates and the times of the incidences when the neighbour has complained not only to the police (they will get fed with him) but also any complaints that he has made to anywhere else.
Make a note also of the dates and the times and the incidences when he has followed you into the garden and simply waits on the other side of the fence waiting for you to knock a nail in.
A civil claim on the other hand does not have to be decided beyond all reasonable doubt but merely, on the balance of probabilities which is 1% more in your favour and you win.
He doesn’t have to harass you directly, he can harass you through a third party by making constant complaints which is what he is doing.
Your remedy is to apply to court for an injunction to prevent him making these spurious complaints against you and to prevent him speaking to you. The threat of that and the threat of court costs might make him be more reasonable although you may find that people like this will think that they are quite justified in doing what they are doing.
That threat of court proceedings and legal costs will have more weight coming from a solicitor.
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