I've seen several mystery buildings going on with people looking the other way it seemed to me.
Sometimes the planners genuinely do not know their own planning law that well, other times it beggars belief that this can go on.
My preferred method - in the absence of any planning permission you could invoke - is to take professional advice on the planning issue arising - it may well be a breach of the exempted development regulations.
There are severe constraints for what can and cannot be built without permission in the curtilage of a dwelling house.
Of course depending on the location the compliance or otherwise may arise from something else, some other schedule of exemption.
For instance the shed may be part of a farm holding, so its best to tread carefully and make no unfounded allegations until you're sure.
Having done that you have ot refer it to the Enforcement Section as noted above, and see if they think it merits opening a file.
If it does they will usually give it an ENF number and write to the alleged offender requesting him to respond with a time period.
A process then ensues which may result in an application for retention, which you could object to and then appeal.
Alternatively they may decide to take enforcement action themselves, but in the current climate the Council have no money.
if they at least confirm there is a breacn of planning law, then you might consider taking a Section 160 Action against the alleged offender.
ONQ.
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All advice on AAM is remote from the situation and cannot be relied upon as a defence or support - in and of itself - should legal action be taken.
Competent legal and building professionals should be asked to advise in Real Life with rights to inspect and issue reports on the matters at hand.