As I mentioned, we do not need to see any debt collector letters. They are irrelevant and can be safely ignored. The only document that has any importance, is the original Notice to Keeper (NtK). The one you have shown us, is not PoFA compliant as it has not been "given" within the required timeframe in order to be compliant with PoFA and so the Keeper cannot be liable for the charge.
The wording is not compliant with the requirements of PoFA either. So, I think it is fair to assume that GPSL are not relying on PoFA to hold the keeper liable. They have no idea who the driver is and there is no legal obligation on the Keeper to identify the driver to an unregulated private parking company.
As for asking the Leisure Centre to get their agent to cancel the PCNs without identifying the driver, all you have to tell them that, as the Keeper, you have received a PCN. They have no idea who the driver is either. A vehicle can be driven by any person as long as they have the owners permission and at least third party insurance. Anyone could be the driver.
You say that as the Keeper, you have received a PCN which has been issued unfairly. The driver was only dropping off your son for lessons at the Centre. No lie has been uttered and the drivers identity is not revealed.
As for the PCNs, easy to defeat... as long as the
unknown drivers identity is not revealed. There is no legal obligation on the
known keeper (the recipient of the Notice to Keeper (NtK)) to reveal the identity of the
unknown driver and no inference or assumptions can be made.
The NtK is not compliant with all the requirements of PoFA which means that if the
unknown driver is not identified, they cannot transfer liability for the charge from the
unknown driver to the
known keeper.
Use the following as your appeal. No need to embellish or remove anything from it:
I am the keeper of the vehicle and I dispute your 'parking charge'. I deny any liability or contractual agreement and I will be making a complaint about your predatory conduct to your client landowner.
As your Notice to Keeper (NtK) does not fully comply with ALL the requirements of PoFA 2012, you are unable to hold the keeper of the vehicle liable for the charge. Partial or even substantial compliance is not sufficient. There will be no admission as to who was driving and no inference or assumptions can be drawn. Gemini Parking Solutions has relied on contract law allegations of breach against the driver only.
The registered keeper cannot be presumed or inferred to have been the driver, nor pursued under some twisted interpretation of the law of agency. Your NtK can only hold the driver liable. Gemini have no hope at IAS, so you are urged to save us both a complete waste of time and cancel the PCN.
Gemini are likely to reject any appeal and, unfortunately, they are IPC members, which means the secondary appeal through the IAS does not have much chance either. The Independent Appeals Service (IAS) is a kangaroo court that only looks after its members interests and is definitely not "independent". You should still appeal to them and any rejection is collated to show the MHCLG why the enacted Parking (Code of Practice) Act 2019 needs to be expedited into effect.