Well, the "other driver" (not strictly true unless you want to throw them under the bus), or do you mean the Hirer (lessee) of the other vehicle? If the vehicle is leased (hired) what has been received is a "golden ticket" because CPM will have failed to fully comply with PoFA paragraph 14.
In your case, not so lucky. You have received a Notice to Keeper (NtK) which is basically PoFA compliant which means that even if the driver is not identified, liability can be transferred to you, the Keeper.
If you want to appeal, for what it's worth, then throw something together and see if you have any luck. When it is rejected, I wouldn't bother with an IAS appeal. That doesn't mean you should pay.
If you really want to appeal it, I would suggest it is done in the ultimate dispute resolution service, the county court. Assuming it ever went that far of course. That is very unlikely.
The most likely successful outcome is any claim eventually issued is discontinued early next year.
Just to clarify, are seeking advice and passing it on to "the other driver" to copy what you do? If their vehicle is leased, it is a different situation from here on. If they want advice on how to handle their "golden ticket", I suggest a separate thread so as not to confuse the two.