Looking at the car park in GSV, why do you think they had reason to believe that they were not obliged to pay for parking at the site? There is a very obvious sign at the entrance that clearly states it is private land and that they could pay by phone or at a machine for the privilege of using the car park.
Not leaving the vehicle does not absolve the driver from being liable to pay for the facility of parking there. They were there for over 20 minutes. Have a read of the BPA CoP where it states about grace periods for consideration of the terms.
No one here likes having to pay the ex-clampers extortionate sums having breached their terms. However, apart from the technical breach of the requirements of PoFA, as explained in my first post, and an argument that the terms notices do not sufficiently bring to the attention of the driver the charge for breaching the terms, I am struggling to see on what additional basis you can appeal. Not that a Plan B appeal would succeed anyway. It has some chance at a Plan C POPLA appeal.