They will reject your appeal if your appeal is based on b789 believing the ntk is not POFA compliant as will POPLA, will need to go to court to get a decision. On the face of it you are exactly the sort of motorist ASDA are obviously trying to dissuade from using their customer car park.
Options are
1. Accept the driver didn't adhere to the terms of the contract and that you can probably be held liable, pay the invoice.
2. Look for another avenue of legitimate appeal, e.g. frustration of contract (car broke down, medical emergency etc. going to a hospital appointment which over ran doesn't count, would need to have been whilst shopping in Asda or similar). Other potential appeals grounds would be defective, inadequate or missing signage, onus would be on you to prove.
3. Rely on the argument that the ntk may not be fully POFA compliant and hope a judge agrees with you.