Only the driver can be liable for the alleged breach of contract they are claiming. They have no idea of the drivers identity unless you, the Keeper, the recipient of the NtK, reveals it to them, inadvertently, or otherwise. If you, the Keeper, refer to the driver in the first person, then it is pretty obvious that you, the Keeper, were also the driver.
If the driver has not been identified, then they cannot rely on PoFA 2012 to transfer liability from the unknown driver to the known Keeper. There can be no presumption or inference that the Keeper was the driver. The burden of proof is on the operator to prove that the Keeper was the driver. The only way they could know that is if the Keeper blabbed it to them... inadvertently or otherwise!
So, if the driver is identified, the "golden ticket" element of the PCN is flushed down the proverbial loo and they can pursue you without having to rely on PoFA. Not that that means all is lost, however, the single point about not being liable, is lost and you would have to rely on a number of other defences such as signage, contract, landowner authority and so on. Also, in most cases, even if a claim is eventually issued, whether directly by CEL or through a bulk litigator, most are either struck out or discontinued.