It would be helpful if someone with an official perspective could answer with authority. The answer at the Instructor Seminar was unequivocal - it's Public Transport.
The CAA have provided an Answer in their latest
PR Campaign
I have been offered a flight as a passenger during a trial lesson. Is this legal?
There is nothing in law to prevent the carriage of non-paying passengers on an instructional flight, apart, of course, from solo flights by a student pilot. If the only payment made is for carriage of the trainee pilot under instruction, the flight is classed as aerial work, and no AOC is needed. However, if any passenger has paid to be carried, the flight is classed as public transport, and is illegal unless the operator holds an AOC.
The last sentence is not strictly correct, because if they held an AOC, the Instruction could not be conducted legally!