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Hi thank you for your message, please note that I will look to provide an accurate but nevertheless speedy reply to your inquiry. I am sorry to hear about your situation but I will endeavour to help you today.
So in essence your dispute is on the basis of where the boundary fence was placed and not necessarily where it should be and the fact that the land registry title plan? Plus the drawings from planning which are not binding anyway.
If you wish to bring a claim about the boundary you need to have the boundary to be known exactly.
It should be noted that determining the true boundary is as not as straightforward as it seems. To prove the true boundary you cannot just rely on land registry deeds as these are not considered accurate enough, the Land Registry for example describe them as approximate boundaries or general boundaries under section 60(1) of the Land Registration Act 2002: https://www.gov.uk/government/publications/land-registry-plans-boundaries/land-registry-plans-boundaries-practice-guide-40-supplement-3.
Determining the true legal boundary depends on the terms of the relevant pre-registration conveyance or the transfer as a whole, including, of course, the plan. If the plan is insufficiently clear for the reasonable layperson to determine the position of the boundary, the court can refer to extrinsic evidence and in particular to the physical features on the ground at the time: Cameron v Boggiano  EWCA Civ 157.
Instead you would have to get what is known as a determined boundary which would involve instructing a chartered surveyor to publish a report and then using that as being the determined boundary i.e. the actual boundary by reference to the plans and the physical lay of the land, you can see more about that here: https://www.gov.uk/your-property-boundaries/apply-exact-boundary-determined
I trust this assists
Let me know if you have further questions