Don’t worry about it. As long as the driver is not identified, you can simply appeal with the following and it will be cancelled:
I am the registered keeper. NCP cannot hold a registered keeper liable for any alleged contravention on land that is under statutory control. As a matter of fact and law, NCP will be well aware that they cannot use the PoFA provisions because Gatwick Airport is not 'relevant land'.
If Gatwick Airport wanted to hold owners or keepers liable under Airport Byelaws, that would be within the landowner's gift and another matter entirely. However, not only is that not pleaded, it is also not legally possible because NCP is not the Airport owner and your 'parking charge' is not and never attempts to be a penalty. It is created for NCP's own profit (as opposed to a byelaws penalty that goes to the public purse) and NCP has relied on contract law allegations of breach against the driver only.
The registered keeper cannot be presumed or inferred to have been the driver, nor pursued under some twisted interpretation of the law of agency. Your NTK can only hold the driver liable. NCP have no hope at POPLA, so you are urged to save us both a complete waste of time and cancel the PCN.