When you appealed, did you identify yourself, the Hirer, also being the driver?
Are you aware that the driver and the Hirer/Keeper are separate legal entities and there is no legal obligation on the Hirer/Keeper to identify the driver to an unregulated private parking company?
As it was a hire car, PPS will have failed to fully comply with all the requirements of PoFA 2012 and thus rendered them unable to hold the Hirer liable for the charge. They had no idea who was driving unless the Hirer (you) told them, inadvertently or otherwise. Only the driver is liable.
So, have you, metaphorically, blown both feet off, leaving you with not a lot to stand on if you intend to progress this to litigation? If so, the only saving grace is that they will most likely use a bulk litigator to issue the claim and, with our advice, we would try and see it through to a discontinuation.