Public Transport Cs of A ceased to exist in Sept 04. All Cs of A are now deemed to be EASA equivalent.
If the flight is unremunerated, it can be conducted in any aircraft in the class, it could be maintained to private or public transport standards, or even be on a permit.
The FI and the aircraft would have to be listed under a Registered Facility, and all flights operated from a licensed aerodrome if the hours are to count; few FIs are likely to own their own aircraft let alone give a studen free flying.
You will also have to complete the CPL written exams and if you want to be paid as an instructor complete a CPL course before you consider the Instructor course.
Getting a sponsored instructor course before getting a PPL is putting the cart before the horse. There is an awful long way to go and it will cost over £20,000