Gentleman or Players
DFC
I'm not sure that you are correct in your example, for this reason.
The fact that the PPL has a Flight Instructor rating means that the club is acting properly in employing the instructor and not paying him/her and is free to make charges as it deems fit. The CAA has no power with regard to club charges to its members and nor should it.
As long as the PPL Flight Instructor does not receive remuneration then they too are acting correctly.