Is the car leased? There is no statutory requirement under the Protection of Freedoms Act 2012 (PoFA) for a Notice to Keeper (NtK) to include the make and model of the vehicle.
The relevant mandatory details are found in Paragraph 9(2) (for postal NtKs), and include:
(a) the vehicle registration mark (VRM),
(b) the date and time of the alleged contravention,
(c) the period of parking (not just timestamps),
(d) the location,
(e) a statement inviting the keeper to pay the unpaid parking charge or, if not the driver, to name the driver,
(f) the warning that the keeper will be liable if after 28 days no payment or driver details are provided,
(g)-(i) details about the parking charge, appeal rights, and operator identity.
Nowhere in PoFA Schedule 4 is the make or model of the vehicle mentioned as a mandatory inclusion.
While not required, including the make and model can support accurate vehicle identification and reduce errors (especially in misreads or cloning cases). If there is a dispute about misidentification or incorrect ANPR matches, the absence of make/model may become relevant evidentially, but not procedurally.
Without seeing the signage, it is difficult to say whether the driver is bang to rights. If you want to fight it, this will go all the way to litigation but is unlikely to actually get as far as a hearing as it would be more likely to be struck out or discontinued, depending on which bulk litigator they use to file a claim.
No initial appeal or subsequent IAS appeal is likely to succeed. That doesn't mean you don't try, even if only to use irritation to the operator who is obliged to respond.
The NtK is basically PoFA compliant, so they can transfer liability from the unknown driver to the known Keeper. So, do you want to fight this?