In your initial appeal to New Gen Parking, try "I wasn't 'parked', I stopped to read your terms and conditions, decided not to accept them, and left"
They'll love that, as all the guidance, whether it's IPC or BPA says that they MUST allow you a grace period in which to read the signage. As long as you were in and out of the car park in under 10 minutes, they wouldn't have a leg to stand on