Show us exactly what your rental agreement says about Parking Charge Notices (PCN), remembering that a PCN is not a "fine" or a "penalty" issued under statutory law. It is simply a speculative invoice from an unregulated private parking company for an alleged breach of contract by the driver.
APCOA are laughing all the way to the bank. All Avis had to do was transfer liability from themselves as the Keeper to you, the Hirer. If they'd followed the law as prescribed in PoFA 2012, they would have then absolved themselves of any liability for the PCN and APCOA would have had to issue you a Notice to Hirer (NtH) in your name. An airport (or train station) PCN is 100% easily defeated as long as the drivers identity is not revealed. There is no legal obligation on the Hirer/Keeper to identify the driver and APCOA (or the hire company) have any idea who the driver is.
So, read this thread and then show us the correspondence from Avis and also the section of the hire agreement that mentions parking charges:
READ THIS FIRST - Private Parking Charges Forum guideYou will most likely have to sue Avis to get your money back, especially if they've breached the hire agreement. Easily done with advice.