Right now you are stuck in a holding pattern, and that is entirely because your V5C address is wrong.
At the moment you do not know whether a PCN has even been issued. Do you even know know which parking company runs the site? You do not have a PCN reference. Without those basics there is literally nothing concrete to cancel, appeal, or challenge. That is not being awkward, it is just reality.
People keep jumping straight to “appeal it” or “get Morrisons to cancel it”, but that all assumes there is an actual charge in existence and that you have the reference number. You do not. Until you know whether a PCN exists, and who issued it, you are guessing. Guessing achieves nothing.
The real problem here is not the overstay. The real problem is service of documents. If a PCN is issued, it will go to the address held by DVLA for the registered keeper. At the moment that address is wrong, and you already know post at the old address is being binned. That is how people end up missing the Notice to Keeper, missing follow-ups, missing a letter of claim, and eventually discovering a default judgment they never knew about. That is the genuine risk you have created for yourself.
So the first and only sensible step right now is to fix the V5C address immediately. Until that is done, you are not “dealing with a parking charge”, you are sleepwalking into a paperwork trap.
Mail redirection is not “too late” just because you have already moved. You can still set it up after a move (6 months, I think). Royal Mail send a notification letter to the old address as a security measure, but that does not prevent redirection being put in place and working. The whole purpose of redirection is to catch mail while you are fixing address records elsewhere. Even partial coverage is better than none.
Once your address situation is under control, the next step is simply to stop guessing. Go back to the Morrisons car park and read the signs. The signs will tell you which parking company operates the site. That gives you a target. Only then can you write to that operator, give them your correct address for service, require future correspondence to be sent there, and ask whether a PCN exists for your vehicle on that date and time and, if so, to provide a copy and the reference number.
Only when you have a PCN reference does anything else become possible. That is when the Morrisons cancellation form (
https://www.morrisons.com/help/form/contact-us/car-park/car-parking-charges/i-have-a-car-parking-charge) becomes usable. That is when a Keeper appeal becomes possible. Until then, there genuinely is sod-all you can do about the parking charge itself, because there is nothing tangible to act on.
So forget appeals, forget clever arguments, forget retailer cancellation for the moment. The priority is boring but critical: fix the V5C address and make sure post can actually reach you. Everything else follows from that.