Please stop redacting dates and times. They need to remain visible if you want a proper assessment of the Notice to Keeper (NtK) and its compliance with PoFA.
Have you approached Sainsbury's to complain about this? That should always be your Plan A. As a customer, you should not be expected to receive a speculative invoice from a third party, unregulated private parking company.
Aim as high up the management food chain at Sainsbury's. Don't expect a lowly customer service bod to know or really care about your predicament. Start with the CEO. Google is your friend for finding out who that is and their contact details.
It is too late to appeal. You can safely ignore the debt recovery letters. All debt collectors can be ignored. they are powerless to do anything except to scare the low-hanging fruit on the gullible tree to pay up out of ignorance and fear of litigation.
If Plan A does not bear fruit, then what you can expect, eventually, is a Letter of Claim (LoC) which will be issued by DCB Legal and then an N1SDT Claim Form from the CNBC, which cannot be ignored.
Show us the LoC when it is received and also the claim. We will provide the necessary advice. Eventually, the claim will be discontinued if you follow our advice and that will be the end of the matter.