The thing I feel everyone has overlooked so far is the existing wall on the shared boundary line so that it can be used?
I doubt it would be on the shared boundary and solely on their property, so there will be zero access to adding to it, modifying or using it. Certainly not without their permission which I can't see they would give... Nor would you want to ask as you'd be responsible for any problems.
So you will end up with the kind of ridiculousness that our ****wit neighbour has bought upon us.
Everything is done on his side so he can do as he pleases without the need to involve or offer consideration to neighbours. I'd expect this would be the same.