...... and it has recently come to my attention that the boundary fence(wire fence) is in the incorrect location in relation to the land registry map. Its off by about 10m.
From this, I take it that the land registry map shows you to 'own' about 10m more of a strip of land outside the fence in question? ( forgive the cynicism, generally if the physical boundary was 10m outside the mapped boundary, people would say "my map is wrong........")
The starting point with an issue such as this is to ask the first and most basic question, as follows:
"The physical boundary is in one place; the mapped title boundary is in another place; they can't both be right; which of them is wrong?"
In other words, the correction of this problem may involve:
a. Moving the fence OR
b Correcting the Land Registry Map
( or possibly a little of both, if things were well and truly cack-handed).
Only when you have answered this first question can you decide how to proceed.
Most of the time, it is more likely to be the case that it is the mapped boundary, rather than the physical boundary, which needs alteration.
But of course, it depends on the actual facts. To take a nice clean theoretical example, suppose you bought a (physically unmarked\pegged) site by reference to a map (which would have been supplied by vendor) and if you ( or the vendor) subsequently put your fence up in the wrong place, then there would be a case for insisting that the fence be moved to the mapped location, as the site was bought solely by reference to the map.
But if the site was already fenced or pegged when purchased and was then incorrectly marked onto a map, I don't think you are quite in the same position.
I hope this helps to clarify your thoughts.