It is not a "fine" so please stop considering it as such. It is simply a speculative invoice from an unregulated private parking company. They have no idea who was driving and have simply sent you, the registered keeper an invoice for an alleged breach of contract.
You are dealing with APCOA who are relatively benign and easily beaten. Nobody who follows the advice pays a penny to APCOA. You must understand that they have no idea who the driver is unless you dob yourself in it by identifying as the driver. Don't.
Because APCOA have not relied on the provision of the Protection of Freedoms Act 2012 (PoFA), they cannot transfer liability from the driver (unknown) to you, the keeper. As such, this is easily cancelled.
Plan A: Go as high up the management food chain at the Tesco and ask them to get the PCN cancelled. Don't expect a Customer Service agent to know how to get this cancelled. Point out that if you are going to be liable for an additional invoice For £70 from a third party, unregulated private parking company, just for being a patron of their store, you may as well take you and your families business elsewhere. Get any communication from them in writing.
If you do get any pushback from the management at the store, you should email the Tesco CEO with your complaint about receiving an invoice for £70 after spending your hard earned money with Tesco. Let his executive team deal with it.
Plan B: You write the following appeal to APCOA without identifying as the driver (do not select any options on their appeals portal that gives away who the driver was. Ideally, send it as a PDF attachment:
I am appealing your Parking Charge Notice (Ref: ________) for vehicle registration mark ____ ___, in which you allege that the driver has incurred a parking charge. As the keeper, I note from your correspondence that you are not seeking to hold me liable under Schedule 4 of the Protection of Freedoms Act 2012 (PoFA). As you have chosen not to issue a Notice to Keeper (NtK) in accordance with PoFA. I suggest that in order to save us both time and money, you cancel the PCN.
As there is no obligation for me to name the driver and no inference can be made otherwise, 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 where we both know, you will lose.
Plan C: If APCOA don't accept your appeal, you then appeal to POPLA where this will be cancelled.
