Have you tried Plan A? Find out who the landowner is. Does the car park belong to a company or business at the location? Someone has contracted UKP and you would need to find out who that is and ask them to get the PCN cancelled.
As for an IAS appeal where the driver has admitted liability, I don’t think there is really any appeal that has a remote chance of succeeding. They will not consider mitigation. They are only going to consider points of law and breaches of the IPC Code of Practice (CoP).
The PCN is an invoice issued because you agreed a contract ‘by conduct’ that if you breached any of the terms on their signs, you would be liable to pay them £100. It does not matter whether you read the signs, as long as they were there, they were prominent and conspicuous, they fully complied with the IPC CoP and any other legal requirements.
If you could show that there is any breach of the legal or CoP requirements that meant no contract could have been formed, you may have a chance, not with the IAS, but at court if this ever escalates to a county court claim. However, you have admitted in the initial appeal that you knew about the overstay and the mitigation you mentioned is irrelevant to the ‘contractual terms’ agreed on.
As I mentioned, you have zero chance that the IAS is going to uphold any appeal, even if you could somehow evidence that no contract was formed. That would have to wait and see if UKP decided to try and sue you for the alleged debt.
They may never do so. Even if they do, they may never actually go all the way to a hearing as these companies often only use the claim process as a last resort to try and pressure the defendant into giving up and paying.
They have six years in which to file a claim.
If you are intent on trying an IAS appeal, then have a look at the IPC CoP and try and find anything they may have breached that you can use to base your appeal on. Also have a look at the Consumer Rights Act 2015 (CRA) for anything that you can use.
The IPC Code of Practice v9Consumer Rights Act 2015