Charge certificates are for council PCNs, no such thing in the private process.
The next step will be a barrage of letters from debt collectors, which you can ignore. If they decide to sue, at some point you'll receive a Letter of Claim, if you do, come back here for advice.
If the worst were to happen and you were to lose, providing you pay on time, the CCJ would be removed from the public record, avoiding harm to your credit score etc.
If you move house at all between now and the alleged debt becoming time barred (6 years from the date of the parking event) and the matter is not resolved, contact the Data Protection Officer at NPM to inform them of your new address.