The driver entered into a contract by parking according to the terms set out on the signs, under which the driver agreed to make payment of some amount for a period of parking.
The driver didn’t make this payment, why not? Are the signs prominent and clear or not? If they are clear, what was the reason the driver didn’t pay properly?
If the signs weren’t clear, then the registered keeper can appeal on this basis, but it’s more than likely the appeal will be rejected, the case will go to court but will eventually be discontinued. It will take a number of months.
Although you, as registered keeper, were not the driver, it has previously been stated that Horizon has complied with PoFA 2012 (
https://www.legislation.gov.uk/ukpga/2012/9/schedule/4) to hold the registered keeper liable for the actions of the driver.
If you appeal, you need a reason for your appeal. What is it? You can’t appeal to the ‘better nature’ of these companies because they don’t have one.
You can also identify the driver if you would prefer Horizon to chase them instead of you.