Thanks for your enquiry.
If your neighbours have a right of way over a designated area of your property, then I'm afraid you are not entitled to "divert" this right without them both consenting.
I note that you say that the existing path is not shown/registered on the Land Registry but if the route of the right is clear from past use, then it is clear that this is the route over which they have a right. Therefore, you do stop them using this route, then you would be breaching their right and they could take enforcement action against you.
Provided both your neighbours are in agreement to diverting the right of way, then a Deed would need to be prepared by a Solicitor showing the existing route of the existing right and the route of the new right, and all parties, including any respective Mortgage Companies, if any of you have Mortgages, would have to sign this Deed, releasing the existing right and agreeing to operate the new right of way. The Deed would then need to be registered at the Land Registry. This is not therefore an easy/cheap thing to do, and is likely to cost you at least £750 plus VAT in legal fees, and more than likely you will also have to agree to pay your neighbours legal fees which are going to be for about the same amount.
I hope this answers your question, and if so, I would be grateful if you could leave positive feedback.
However, please let me know if you require any further assistance.