By the letter of the law it could be argued that the car parked in the car park was not paid for, so the charge could be applied, but we would suggest following the appeals process and hope that they take a reasonable approach. Include the evidence that you paid for another car in error, as their records will indicate that the incorrectly paid-for car was not present in the car park at the time and you had no intent to avoid paying the parking charge. However, in our own experience, they are unlikely to cancel the fine. Car parking firms rarely show much in the way of reasonableness.