A freelance instructor would need to Register in order to train a person on their own aircraft.
As the Rules for the NPPL have not been written knowbody knows.
The Reference to a Flying Club is one of the terms under which the holder of a BCPL(R) and in certain cases a PPL holder may be remunerated without holding a Commercial Licence.(Eg Helicopter and Microlight Instructors) It is written into the Restriction contained in a BCPL(R).