Being the sceptic that I am, I looked into it myself and true enough, building extensions up to 40sqm did not require PP....unless....the extension building has a window that overlooks another property whose boundary is within 11metres of the extension.
In the OP's case the structure isn't an extension, so is not covered under exempted development.
You may have some scope in that regard for some monetary compensation, but I would expect between legal costs and challenges (and peace of mind) it would not be worth it.
Getting the structure removed is the only recourse here. Lodging a complaint to the LA is free.