There is no "offer" in that sign. There is no mention of parking. There is no mention of how a permit can be obtained. There cannot have been any contract.
As you are dealing with an IPC member company, this is not going to succeed at any appeal stage. The only way this will be won is if they decide to pursue you through the courts for the alleged debt.
They may never bother to take it all the way to court as they would receive a spanking due to their CRA breaches and their lack of contract. That does not mean that they are not going to try and scare you into paying into their scam with debt collector letters.
DRAs are powerless to do anything and are employed to simply try and scare the low-hanging fruit on the gullible tree into capitulating and paying into their scam. They can be safely ignored.
The way forward as I see it is to make a simple appeal as the keeper, which will be rejected. In the appeal, you deny any liability for the charge, pointing out the deficiencies and you also warn them that if they do not cancel the PCN, they should proceed directly to issuing a claim in the county court where you will vigorously defend and claim. You do not wish to participate the kangaroo court IAS secondary appeal and they must not pass your data to any third party DRA.
They are likely to ignore it all but they are now n notice that they do not have your permission to pass your data on otherwise they will be in breach of your GDPR and then liable to damages. We do want them to issue a claim as that is the only way this is put to bed.
In the very worst case scenario, there is a minute risk that should it proceed all the way to a hearing and your defence was not accepted by the judge, you would be liable for around ~£200 max, which if paid within 28 days of judgement has no effect on your credit file and is completely expunged fro the record. So, no risk of a CCJ on your file.
The most likely outcome is that they try and scare you into paying which you ignore. They then have to decide whether to litigate and that is a big risk for them. It will cost them to file a claim, which will be easily defended. The most likely outcome once the defence is filed is they either discontinue before they have to pay the hearing fee or that their claim is struck out.
It is for you to decide how you want to proceed. The advice is to appeal in the first instance to NPM and then wait and see what they decide to do after they reject the appeal.
This is what I suggest you put in your appeal:
As the keeper of the vehicle, I decline to identify the driver. I deny that I owe any debt and challenge the Parking Charge Notice (PCN) [PCN Number] issued on [Date] at [Location], in which you allege that the driver is liable to pay a parking charge to you, National Parking Management Ltd, as the creditor.
The driver has not breached any contract as the signs at the location do not make any offer. The driver took less than 4 minutes to consider the terms and decided to leave. Therefore, I suggest that the PCN be cancelled immediately.
I do not wish to engage in a secondary appeal through the Independent Appeals Service (IAS), as their reputation as a biased and non-independent body makes it a waste of time for all parties involved. Any offer of such an appeal will be disregarded.
Please take careful note, as this appeal will be used in evidence should this dispute ever reach court. If you refuse to cancel the PCN, there must be no passing or transfer of my details to a third-party debt recovery agent (DRA). Instead, you should issue a claim for the alleged debt in the County Court, where I will vigorously defend myself and you can expect a thorough examination by the judge.
Furthermore, any deviation from this requested path, including involving a third party for debt collection, will be considered harassment under the Protection from Harassment Act 1997 and a breach of GDPR under the Data Protection Act 2018. Such actions may result in a Part 20 counterclaim against you for any distress and inconvenience caused by these breaches.