Hi, this is Jim, thank you very much for the question - I will do my best to resolve this for you today.
If the survey confirms the fence goes over in to your boundary, the neighbour is currently trespassing. As such you can apply to the local county court for a civil injunction.
However, before you do this, send the neighbour a cease and desist letter to warn them of your intentions unless they agree to move the fence back (and give them 7 days to confirm they will do so). 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 the trespass, and that if they do not confirm they will move the fence back 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.
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 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 the tort of trespass. You can attach the survey report to the application.
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.
I hope this helps - please feel free to ask me anything else.
Have a good day,