If you do a search on here on airport you will see that they are covered by bylaws, and therefore not relevant land for POFA purposes and the parking co have no route to transfer liability. In your case, it being a hire car adds a further layer of complication - presumably there were no accompanying documents with the NTH? In general APCOA don't litigate, and often roll over if a decent appeal is put before them. You have 2 points:
1. Airport so not relevant land and there is no route via POFA for transfer of liability
2. Not withstanding 1, the vehicle was on hire, and they have not supplied the required paperwork to transfer liability, so even if 1 didn't apply, they would not be able to hold the hirer liable.
Just make sure in any appeal you do not identify the driver, even incidentally by saying 'I did'!