Sounds as if your 'structure' might straddle the boundary. I don't think it's necessarily relevant that it's a garden shed rather than part of your house.
Perhaps he should have served you a party wall notice before he started?
I don't really know anything of course, and I expect that rabbit hole could be a large warren.
When I demolished my house and cleared the site, I 'found' a boundary wall that had been enveloped by shrubs. It was in poor condition, quite low, and single skin. Stupidly I told the digger driver he might as well take it out.
Of course, it turned out to have been my neighbours wall (it was there before my old bungalow was built, apparently) and he had seemingly been quite attached to it so I was on the hook to replace it. Had I left it, the falling down wall wouldn't have been my problem.
Fortunately my neighbour is a reasonable bloke, for a farmer. I built an improved wall, and he took about 180 tons of surplus muck away for me.
On reflection, we should probably have had a party wall agreement. Luckily we seem to have resolved it.
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