AFIK the general rule is that if the payer dictates when and how the job is done HMRC will view it as employment. If the worker decides it then it can be treated as self employment.
Example
You pay someone to paint your house. He provides the materials and does the job his way to his own timetable, self employment.
You obtain paint ladders etc and employ someone to do the painting at an hourly rate under your supervision at set times, employment.
I suspect that the pitiful wages of FI's mean HMRC have more rewarding targets to pursue.
WRT clubs owned by their members. They are generally companies limited by guarantee with each member typically guaranteeing one pound, which is the most they can be called on to pay. The clue is in the word "limited".
As for schools run as charities, I'd love to see one that's registered with the Charity Commissioners!