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.
The setup is different to what I imagined, having now seen the photo. No actual path is demarcated. Would be interesting to know if I have the boundary line in the right place.
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.