Hopefully, you didn't actually reveal the identity of the driver when you mistakenly contacted the debt collector. Under no circumstances should you reveal the drivers identity until we know more about the circumstances of the parking event. Any contact with the parking company should be as the Registered Keeper (RK) as that is who they are communicating with. Unless you revealed the drivers identity, they have no idea who that may be.
The RK and the driver are two separate entities in law. Until we can see a copy of the original NtK/PCN allegedly sent to the RK, we don't know whether only the driver is liable or either the driver and the RK.
What was the location? Which unregulated private parking company is supposed to have sent the speculative invoice that you never received? That info should be on the correspondence you received from the debt collector.
Do not contact debt collectors. They are not a party to the contract between you and the parking company for the alleged breach. Most of these debt collector companies operate on a no-win, no-fee basis and their modus operandi is to intimidate the victim into paying the now enhanced charge.
You can ignore the debt collector as they have no powers to initiate any legal action and all the bluster about CCJs and bailiffs is purely designed to get low hanging fruit on the gullible tree to capitulate and pay up.
For now, you may want to have a look at your V5C registration document. Is your current address up to date on it?
It is a common mistake for many motorists to update their drivers licence details when they move but forget to update the V5C, which is where the parking company gets the registered keepers information from the DVLA. If that's the case, the debt collector probably used a simple credit trace to get the current address.
Which parking company are the debt collectors representing? It is almost certainly too late to appeal to the parking company and, depending on which Approved Operator Scheme they belong to, BPA or IPC, it is also likely too late for a secondary appeal to POPLA or the IAS. Never mind... the whole process is flawed anyway.
Have you tried to contact the landowner where the alleged parking event happened? That is what is known as Plan A and often gets the PCN cancelled. Plans B and C, as already mentioned, are most likely a no-go at this stage. Ultimately, Plan D, a hearing before a judge who will ultimately decide whether you owe the parking company a debt, is the most likely to succeed in seeing this off.
For now, please advise which parking company and the location of the car park and the circumstances that you think may have caused the PCN to be issued.