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It's difficult to tell from the plan, but there aren't any easements/rights shown. So the path is on one person's land or the other's.
Fence along the boundary. If that doesn't solve it - because the access path is on the neighbour's land - then gubhi doesn't have much of a leg to stand on anyway.
Anecdotally, our shed is on our upstairs neighbour's land, technically, because it's under the outdoor steps from their roof terrace to their part of the shared garden. That strip of land is shown as blue on the deed plans.
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It's difficult to tell from the plan, but there aren't any easements/rights shown. So the path is on one person's land or the other's.
It is difficult to tell from the plan. Sometimes the Land Registry colour rights of way. Sometimes they don't. In most shared paths between houses I've come across, each house owns one half of the path and has a right of way over the other half. Impossible to say from the plan whether this is the case here though.
That would be an ill-advised move, being entirely illegal if the fence was between their driveway and their half of the shared path.