Name changed just in case.
The boundary in dispute has been damaged by Doris. It is a fence on top of a retaining wall and the wall stops our house sliding down the hill.
It is our neighbours responsibility but he claims it is ours (in which case get your shabby lean to off it) and we should be responsible for the repairs.
The thing is, it may be to our benefit to own the wall as he didn't allow the previous resident to install a gate post on top so we have a gate that is hobbit sized and can barely fit a wheelie bin through.
To make it clear, he is not claiming we have the entire length, just the bit damaged by Doris. He wants to keep the sections either side 
Advice please? Change the boundary legally and do what we want (and can we ask him to remove the eyesore lean to); or show him the deeds where it states it is not our responsibility?