The responsible authorities would be your local planning authority, and the CAA - who delegate most of their responsibilities in microlight training to the BMAA.
The PFA/LAA wouldn't have any interest, and don't even have any interest in trying to merge with / take over the BMAA any more.
I should start with the BMAA since, unlike your local planning authority, they'll start from the point of view that microlight schools are a good thing.
G