Hello, my name is ***** ***** I am a qualified lawyer happy to help you today.
Your legal remedy would be to apply to the local county court for a civil injunction. An injunction serves to either stop someone from pursuing a course of action, or forcing them to do something (e.g. ensuring free access to a property).
However, before you do this, send the neighbour a cease and desist letter to warn them of your intentions unless they give you a key (and give them 7 days to 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 give you a key, and that if they do not within 7 days you will apply to the court for the injunction and seek your costs. Note: you are very likely to succeed if you can show a right of way with the deeds to the property.
That letter may well be enough to resolve this - 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. That fee is recoverable from the neighbour.
You will need to prepare a witness statement to accompany the form to detail the issue, the description in the deeds, and your remedy sought.
The court will list a hearing where you attend and ask the District Judge for an order and the injunction.
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 - 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.