I don't see any "letter before action" in there. Only a response to your communication with Gladstones. The "final chance before action" is not a Letter of Claim (Loc) and it is unlikely that it would come from CPM. They would use Gladstones or some other bottom-dwelling bulk litigation company to do that.
You mention that "my name is now up to date on the V5C". Was it not correct at the time of the alleged parking event? If there is even a remote possibility that CPM or Gladstones hold two possible addresses for you, you must send an email to the DPOs of both companies, instructing them to update their records with your current address for service and for them to erase your old address and to confirm when they have done so.
Simply updating your v5C after you have received an NtK does not mean anything to the PPC because they are only allowed a single bite at the DVLA cherry for your data. You do not want them holding an old address when you may miss a vital letter and end up with a CCJ by default.
We also need a bit more information for context. You show a permit in your photos. Why was the vehicle parked at the location? Is that where you live? Is the permit issued by CPM or via the management company or landlord?
