The Police don't sound like they have done much if they simply took the neighbour's word for it and didn't investigate this.
There is a further option and that would be to apply to the local county court for a civil injunction. This is a civil court order which prohibits a course of conduct such as antisocial behaviour. If you rent or the neighbours rents, you can ask the local council if they can deal with this as they can apply for an injunction on their own behalf.
If you have to apply then you should send the neighbour a cease and desist letter to warn them of your intentions unless they stop (and give them 14 days to stop their conduct to allow them to seek legal advice). A template “cease and desist” letter is available at LawDepot
If you go to the search box in the top right corner of the site, it will bring up a list - you want the "general" letter.
You can use your own letter if you wish - it just has to make it clear this is a cease and desist letter, that you demand they stop their conduct, and that if they do not within 14 days you will apply to the court for the injunction and seek your costs.
That letter may well be enough to stop the conduct - as an injunction is a serious legal remedy. The judge will want to see that you have sent the cease and desist letter given an injunction is a last resort.
Assuming they continue, you will need to complete the application for the injunction and send to your county court.
You will need to detail the history of the issues with the neighbour to paint a picture for the Judge as they will not know what this neighbour is like and what they have done to you unless you describe it.
If the injunction application is successful you can ask the court for a costs order to be paid by the neighbour.
The court will list a hearing where you attend and ask the District Judge for an order and the injunction. The application would be made under Section 1 of the Protection from Harassment Act 1997. Harassment is defined as “unwanted conduct designed to cause the victim alarm or distress”. There needs to be more than one incidence of the harassing behaviour but based on your question it seems that to be the case so you would be fine with applying in my view.
If granted, the Order is then served on the individual concerned and they are bound by the court order - if they breach the order, they are in contempt of court and could well face a fine and a prison term. The order will say they must stop their conduct with immediate effect. They are very effective given the consequences of breaching the terms of the injunction.
The cease and desist letter will hopefully work so you may not need to apply but if you then I recommend you ask one of the following law firms to step in - they should be able to claim their costs from the neighbour so would be worth asking them to help you with this: