Starfish 4,
Your neighbours seem to be engaged in something that may amount to adverse possession and may or may not infringe on registered title or a private right of way.
The wall you refer to may be the built boundary, but as an adjoining owner you may have rights to pass and repass over land outside this wall, assuming yor neighbours's assertions are correct.
Ironically your neighbours' actions in claiming what may have been a right-of-way may in fact limit you exercising your rights over the same right of way, should you in fact have any such rights.
Normally there is accord amongst the neighbours when something like this is done, but it should be done correctly, legally with deeds of rectification, to avoid problems that may arise at sell on with a flawed title document.
ONQ.
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All advice on AAM is remote from the situation and cannot be relied upon as a defence or support - in and of itself - should legal action be taken.
Competent legal and building professionals should be asked to advise in Real Life with rights to inspect and issue reports on the matters at hand.