As long as the driver has not been identified, they cannot hold the Hirer liable. They have no idea who the driver is unless the Hirer blabs it to them, inadvertently or otherwise.
Did you appeal? If you did, did you identify the driver by saying things like "I did this or that" instead of "the driver did this or that"?
Besides the fact they the Notice to Hirer (NtH) is not PoFA compliant with paras 13/14, the location is not relevant land as it is covered buy statutory byelaws. As long as the driver has not been identified, this will go nowhere.
As already mentioned above, because ParkingEye are using DSCB Legal, they know they don't have a chance if this ever went in front of a judge. If DCB Legal do issue the claim, you will defend using the template defence we provide and I can guarantee that it will eventually be discontinued. They only go this far because they hope you are low-hanging fruit on the gullible tree and can be intimidated into paying out of ignorance and fear.