What exactly does the wording in your hire agreement with ZIP say about parking charges? Remember, it was not a "fine" nor a "penalty" from any authority but a simple invoice for an alleged breach of contract between the driver and the PPC.
As already noted, the issue is now between you and ZIP. The PPC is laughing all the way to the bank. If ZIP did not have the right to pay an invoice from an unregulated private parking company because the terms you agreed and signed with them for the car, then you have valid grounds to sue them in the county court.
Unfortunately, for you, this is not really a "parking" issue but a Consumer Rights issue.
