Unless this is a car park on land that is under statutory control, you will not receive and "Penalty Notice". If it was a car park on private land that is not under statutory control, then you would receive a "Parking Charge Notice" (PCN), which is simply a speculative invoice for an alleged breach of contract by the driver from an unregulated private parking firm.
If the latter, then as long as payment was made for the applicable duration, they should not issue a PCN. The PPSCoP was revised in February this year to cover that eventuality. Annex F.1(j) applies.
If you do receive a PCN, then come back and we can advise on how to deal with it then.