Well it seems I was wrong about the driver/keeper, they only have right to charge the Driver.
This is actually a minefield:
Try this link:
FAQs - Private Parking Companies/Charges (everything you need to know)
The long and the short of it is, as I understand it now,
yes you are legally liable for fine, if you admit you were the driver and you were aware of the parking restriction and entered into a "contract" with them by parking there and understanding the terms of the parking agreement.
But.... if you refuse to admit you were the driver or you were aware of the terms of the contract, then the onus on them is to prove all that, which they are unlikely to be able to do. So you basically have a loop hole to "get off" by lying, playing silent, and not cooperating. As usual the law is a bit of an ass!
This is only true for a private enforcement company. Public authorities and the police have much greater powers to get you!