Whatever you do, do not identify the drivers details. The NtK (PCN) has been issued to the registered keeper (RK), In law, the "driver" and the "keeper" are two separate entities.
(Not so) Smart Parking do not use PoFA and so cannot hold the keeper liable. Only the driver can be held liable and they have no idea who the driver is. Even if they had a high resolution picture of the driver, they still would not know the identity as there is no magical database the can use to try and compare a photo to with details. Besides that, they are not allowed to forensically try and identify someone from any such image. Only the police or an "authority" can do that and then only under criminal law. This is a simple civil law case.
One other thing about (not so) Smart Parking is that if this is for parking in an NHS Trust location such as a hospital, they have no contract to issue claims in their own name. This will go nowhere, especially if you follow the advice.
The first thing you must do is try Plan A, which is contact the landowner (if it is an NHS Trust site then contact PALS) and complain and ask them to get this cancelled. Following this, you move on to Plan B, which is an appeal to (not so) Smart Parking.
Under no circumstance identify the driver. No "I parked..." or "I drove..." etc. You are only appealing as the keeper of the vehicle. Do not select any options on their website that asks if you are appealing as the driver.
Use the following in your appeal:
This is an appeal by the registered keeper - No driver details will be given. Please do NOT try the usual Group Nexus Trick of asking for driver details in order to get around the fact your NTK does not comply with POFA. As there is no keeper liability then liability cannot flow from the driver to the keeper and thus is an automatic win at POPLA. Therefore, please cancel the notice or issue a POPLA code at which point you will auto withdraw.
Whilst (not so) Smart Parking will probably reject the appeal, not before trying to tell you that you must identify the driver (which you will not) otherwise they will have no option to "presume" that you were driving, just ignore that and move on to the POPLA appeal where you will win this.