All good points.... and you need to check the titles and conveyances.
If there are double T's on boundary features they are usually considered to be Party.
If there are no T's on boundary features they are also usually considered to be party boundaries unless you can show that the feature is built on one side of the boundary and not straddling it.
Generally if a feature (ie garden wall or fence) is built across a boundary then it becomes a party wall fence (also defined in the act). If a building is built across the boundary or up to the boundary then it becomes a Party Wall structure Type A and Type B and the neighbour has a right for support through the Party Wall act.
To confuse things even further the LR only show general boundaries on their plans and these are normally drawn at 1:1250 scale, so a 1mm line on a plan can be 1.25m on the ground, and much larger that width of most walls and fences......
And more confusion comes if someone builds a garden wall or building on your land by mistake (or on purpose - land grabbing) without your permission, then the structures which are trespassing become part of the land they stand on, and no longer belong to the neighbour, providing Estoppel does not apply.......
Yes, it is all about interpretation and reading what is in the Titles and Conveyances....
From what has been written I have an interpretation with caveats.
Without seeing the Titles and Conveyances it is not clear who owns what.