Welcome to FTLA.
As Luton Airport is subject to byelaws, it is subject to "statutory control", and as such, not relevant land for the purposes of Schedule 4 of the Protection of Freedoms Act (https://www.legislation.gov.uk/ukpga/2012/9/schedule/4), meaning they cannot hold the keeper liable. You could therefore appeal along the lines of the below:
Dear Sirs,
I have received your Parking Charge Notice (Ref: ______) for vehicle registration mark _______, in which you allege that the driver has incurred a parking charge. I am appealing as the registered keeper of the vehicle. There is no obligation for me to name the driver and I will not be doing so. I note from your correspondence that you are not seeking to hold me liable as the registered keeper, under Schedule 4 of the Protection of Freedoms Act 2012 ("The Act").
Even if you were seeking to do so, as the Luton Airport Pick Up / Drop Off Zone is not "relevant land" as defined by The Act you are unable to recover the charge from me, the keeper.
I am therefore unable to help you further with this matter, and look forward to your confirmation that the charge has been cancelled. If you choose to decline this appeal, you must issue a POPLA code.
Yours,
If appealing online, be careful there are no drop down/tick boxes that cause you to identify who was driving, and keep a close eye on your spam folder for their response. If they do not respond within 28 days, chase them. Please let us know when you get a response.