There is no Keeper liability if the driver is not identified for the reason given above. Whilst you, as the named recipient of the Notice to Keeper (NtK) cannot be liable for the charge if the driver is not identified and you have even stated categorically that you were not the driver anyway, you will have to go through the appeals process or initial appeal, rejection, POPLA appeal, possible success. Anything beyond that we will cross that bridge if we ever come to it.
The simple fact is that MET have issued you a speculative invoice for an alleged brach of contract by the driver who is unknown to them. There is no legal obligation on you, the Keeper, to identify the driver to an unregulated private parking firm. Because the location is within the official Stansted Airport boundary, it is land that is covered by airport byelaws and therefore no "relevant land" for the purposes of PoFA 2012, which means that the Keeper cannot be liable for the charge if the driver is not identified.
For now, simply appeal with the following, only as the Keeper and come back for the POPLA appeal once they reject that:
I am the registered keeper. MET cannot hold a registered keeper liable for any alleged contravention on land that is under statutory control. As a matter of fact and law, MET will be well aware that they cannot use the PoFA provisions because Stansted Airport is not 'relevant land'.
If Stansted Airport wanted to hold owners or keepers liable under Airport Bylaws, 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 MET is not the Airport owner and your 'parking charge' is not and never attempts to be a penalty. It is created for MET’s own profit (as opposed to a bylaws penalty that goes to the public purse) and MET 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. MET have no hope at POPLA, so you are urged to save us both a complete waste of time and cancel the PCN.