We were somewhere around Barstow, on the edge of the desert, when the
drugs began to take hold. I remember "Harry Syme"
saying something like:

so does anyone know the answer to my original question..

Can I complain about this and which council department would I contact ?
Or

I doubt if the council will be interested, as a garden shed wouldn't
fall within their remit.

does it have nothing to do with the council and would a private civil action
need to be taken? Or a small claims action?

I think you'd be in the realm of getting the Factor off his arse and
then going to see a solicitor, if necessary. You have to knock on every
door in the close to get all the other neighbours' take on it. Some of
them might not care or shy away from potential legal costs.