Whilst the advice from
@DWMB2 is the all important Plan A where you use your initiative to complain to the hotel about the actions of their agent, an unregulated private parking company issuing you a speculative invoice for an alleged breach of terms, you should also consider what you need to be doing for Plans B, C and D.
Plan B would be an appeal to Britannia Parking. However, we do not know whether they are attempting to hold you liable as the driver or as the keeper of the vehicle. Without showing us the original NtK you received, we may never know. What you must not do, until we can be sure, is identify who was the driver. For now, you are being pursued as the keeper. Unless you have identified as the driver, they have no idea who that may be and no assumptions can be made or inferred.
If your Plans A and B are unsuccessful, Plan C will involve an appeal to POPLA. You cannot proceed to Plan C without first completing Plan B.
However, you do have something that I can see in the NtK reminder (assuming that the same evidence is in the original NtK) that a POPLA assessor may take into consideration which would invalidate the PCN. The evidential photos used must bear an accurate time and date stamp applied at the point the picture was taken. Whilst the originals may contain a time stamp, the ones we can see in the reminder have been cropped and do not show any evidence of when they were taken. As long as the original NtK has the same images, it would be worth pointing out to a POPLA assessor and you could quote them to refer to the recent POPLA decision (2413353469).
Any POPLA decision is not binding on you if you were to be unsuccessful. That would leave Plan D which, if Britannia Parking want to, would lead to a county court claim where it would be up to a judge to decide whether you owe them a debt or not. That is an if/when scenario and a long way off, if ever, for now.