As long as the Keeper has not been identified as the driver, then they have nowhere other than go with this. The dumb thing was trying to appeal it in your name as the driver when it was not addressed to you!
The Keeper cannot be liable for the charge because there can be no Keeper liability for an alleged contravention on land under statutory control, such as byelaws, at an airport. At the time a simple appeal as the Keeper referring them to the answer given in
Arkell v Pressdram (1971), reminding them that the location is not relevant land would have sufficed and it would have been cancelled.
However, this has been SNAFU'd and now you are going to have to waste a load of time and effort if the utter incompetents at Moorside Legal issue a claim, which is highly likely. Just continue to ignore everything, especially debt recovery letters because debt collectors are powerless to actually do anything except to persuade low-hanging fruit on the gullible tree to pay up out of ignorance and fear.
When the Keeper receives a Letter of Claim (LoC) from the morons at Moorside Legal, come back and we will provide a response.