Assuming the Police (on the 101 number) do not think the harassment is serious enough to warrant prosecution, there is another option which is to apply to the local county court for a civil injunction. You should try the Police first though.
However, before you do this, send the harasser a cease and desist letter to warn them of your intentions unless they stop (and give them 7 days to stop their conduct). A template “cease and desist” letter is available at https://www.lawdepot.co.uk/
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 7 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.
This needs to be posted as well as emailed. I note you only have their name - and they change their email addresses. You need to know how to contact them here so the court can serve an injunction order against them. You may need a tracing agency (most offer a no trace no fee service), here are a few options:
Once you have sent them the letter and assuming they continue, you will need to complete the application for the injunction and send to your county court with a fee of £308 payable to HMCTS (unless you have a low income/low savings and/or you are in receipt of benefits in which case you can get a fee exemption so you do not have to pay).
For a fee exemption you need to check your eligibility here:
http://www.gov.uk/get-help-with-court-fees. If you do not qualify for the fee exemption, you can pay either by cheque or attend the court and pay at the counter. You will need to prepare a witness statement to accompany the form.
You will need to detail the history of the issues with the harasser to paint a picture for the Judge as they will not know what this person 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 harasser.
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”.
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 cease and desist letter may work so you may not need to apply but if you then I recommend you go to the court in person with the forms to ensure they are correct - they are fairly complex so it would save time by you doing this - the court staff should check them before they issue the papers.
If you do need to take that step and apply for the injunction, please come back here as I have the forms required.
To answer the query about effectiveness - it is very effective because they go to prison if they breach the terms of the injunction.
I hope this helps - if you can please accept the answer and give me a 5 star rating (there should be a button at the top of your screen to do this), I can answer follow up questions at no extra charge and Just Answer will credit me for helping you today.