As above. Your plan A is to get the gym to call of their contracted dogs. If you're now receiving debt recovery letters, it is too late to appeal. Your fault for not updating your V5C.
Even if you have since updated your V5C, that makes no difference. You must send the parking operator DPO a Data Rectification Notice (DRN) instructing them to update their records with your current address for service and to erase your ol address. The highlighted words are there for a reason, so use them.
Failing to do that is a surefire way to get a CCJ by default.
We are not interested in any debt recovery letters from powerless and useless debt collectors. Never, ever, communicate with a debt collector. They are not a party to any contract allegedly breach by the driver. You can safely ignore them. Their only job is to try and scare the low-hanging fruit on the gullible tree into paying out of ignorance and fear. Ignore them.
Please show us at least one of the Notices to Keeper (NtK) you received. Do not redact any dates other than times.