Don't be low-hanging fruit on the gullible tree. Your appeal is borderline giving away the drivers identity. Always refer to the driver in the third person. Never "I did this or that", always "The driver did this or that".
The Notice to Keeper is addressed to the known Keeper, you, I presume. However in your appeal you go on about how you, the Keeper are prepared to stand in front of a judge and prove the drivers innocence.
If only you'd come here first before making a futile appeal to UKCPS and then the even worse IAS. The Notice to Keeper (NtK) is not fully compliant with all the requirements of PoFA, specifically paragraph 9(2)(a). This means that the Keeper cannot be liable, only the driver. UKCPS have no idea who the driver is unless the Keeper blabs it inadvertently or otherwise.
Also, the driver cannot have entered into a contract with UKCPS if the signs are prohibitive. A contract requires three elements, an offer, a consideration and an acceptance. "No parking permitted any time" does not offer anything and therefore there is nothing to consider which leads to the fact that there was no acceptance.
Had there been a contractual offer that could be accepted, the driver would have been allowed a "consideration period", which has a minimum period defined in the BPA/IPC Private Parking Single Code of Practice (PPSCoP). The NtK does not show that any "period of parking" has been recorded, hence the breach of PoFA 9(2)(a).
Anyway, you are where you are now. There is nothing more you can do for now. You are going to have to wait and see if/when they issue claim. You can safely ignore all Debt Recover Agent (DRA) or debt collector letters. They are not a party to any contract that the driver allegedly breached. They cannot do anything. Never, ever, ever communicate with a useless DRA. They are powerless and can be safely ignored.
If/when you receive a Letter of Claim (LoC), which will differ from the useless DRA letters as it will give you 30 days to pay rather than the tiresome DRA letters which only give 14 days, come back and we will advise on the next steps and how to deal with it.
No one who is here receiving advice and following it pays a penny to ex-clamper scammers like UKCPS.
If you want to mess with their intellectually malnourished minds, you could send them a formal complaint and require them to respond, which really cheeses them off as they are obliged to respond, then let me know and I can provide a template for you to send.