You have already identified yourself as the driver, so there is no value in arguing about keeper liability or PoFA. Napier do not need PoFA if they can pursue you as the driver on a contractual basis.
On the face of it, their paperwork and the signage are at least broadly aligned. The sign makes it clear that the “duration of stay” is calculated from the point of entry to the point of exit, and it states a £100 parking charge for breach of any term. The NtK then alleges an “overstay of paid for parking session” and relies on ANPR entry and exit times to calculate the total stay. So the NtK is not obviously pursuing a different basis from the sign; it is applying the sign’s “time on site” model.
However, there may still be mileage in a contract-based challenge, but it is fact-dependent and it is not a technical PoFA point. The strongest potential angles are:
1. Incorporation and prominence of the key term. If the entry-to-exit timing term was not sufficiently prominent at the entrance and/or was not reasonably readable before you became committed to parking, you can argue that this key term was not properly incorporated into any contract.
2. Unfairness and lack of a reasonable means to perform the contract. Your central point is that you paid for four hours and only overstayed by around twenty minutes, and the payment system apparently jumped from four hours to twenty-four hours. If, at the material time, there was no reasonable mechanism to extend the session or pay the additional time, and this was not clearly explained on the signage, you can argue that the way the terms operate is unfair because it exposes a consumer to a £100 charge for a modest overrun when the consumer has no practical way to comply.
3. Authority and standing. Even if you were the driver, Napier still have to have proper landholder authority to offer parking on those terms and to enforce charges in their own name, and they must prove the vehicle was in the part of the site covered by their signage and contract.
If you want to run this as a contract dispute, the focus should not be “PoFA” but evidence. You need photos of the entrance signage, the payment machine/app screen showing the tariff options at the time, and the terms displayed on-site. The argument then becomes: the key terms were not properly brought to your attention and/or the payment system and terms were not fair or transparent because you could not reasonably pay for the small additional time needed.
Napier usually use the utter incompetents at Gladstones to issue their claims, which means you can guarantee that they will not comply with CPR16.4(1)(a) which always leaves the claim open to a strike out.