Posted: 17/02/2018 at 14:21
There is no need to get your neighbour to sign a piece of paper. The wall is entirely on the OPs property, not on the boundary line so the neighour has absolutely on right to touch it, as explained by Freddies Dad above.
Where the OP is going wrong is by charging in and making threats of legal action. It's entirely likely that the new neighbour just assumed it was the boundary line if the old fence was removed before they moved in. All it needed initially was to inform the new neighbour that they couldn't do anything to the wall without permission.
I've had personal experience of similar problems. One where new people moved in next to my mother and promptly ripped the boundary fence down at the side of mum's garage and started screwing and hammering all sorts of things to it. The garage wall was at least a foot inside the boundary line so we informed them very quickly that (a) they shouldn't have taken the fence down as it was mum's property and responsibility according to the deeds and (b) they had no right to encroach on her property.
The second was where I had a snotty note pushed through the letter box from the people in the house which backs onto us, demanding that I cut a tree down because it was blocking light from their garden and all the leaves fell into their garden in the autumn. The tree was actually in their garden but, because a previous occupant had decided they wanted more privacy, they had built a 6' decorative block wall about 2 feet inside their boundary (the old fence was, and still is, there). The tree had grown between the block wall and the fence. I actually enjoyed telling them that and watching their faces drop when they realised that removing it was their own problem. I would have happily helped if they hadn't been such ***holes.