The "appeal" process is part of the scam for private parking charges - they're not independent despite what they claim and they almost never succeed. Participating in the appeal just reinforces the notion that a fair consideration of the facts has taken place.
By agreeing to be bound by the outcome of their pretend appeal system you risk making yourself liable if it goes to court. They try and make what they do look as "official" as possible but their claim has little more basis than me putting a sign on my garden gate that says entering my garden will incur a fee of £10 and entering the garden means you've accepted that charge. You haven't been "fined", you've been sent an invoice made to look like a fine.
For future reference, complain to your MP and local councillors about the company behind it - you never know when action is already pending against certain companies and your case may help tip the balance. I found this when the same thing happened to me - the car park was gone within six months and the enforcement company ceased trading.
Rather than fall into line with the bogus review and appeal process, write back to them stating that you do not accept their claim, as a contract was never formed and you look forward to seeing them in court. They'll send you threatening letters, they may get a debt collection agency to try and frighten you etc but ultimately it's not up to them to decide whether you owe them money or not and they often don't bother going to court because a) it's not worth their time and b) they don't want to lose too many cases as it'll undermine their chances of continuing their scam.
As stated earlier in the thread DO send them a schedule of your charges for dealing with their correspondence and tell them that if they contact you again they will have signalled their acceptance of YOUR T&C's and will be charged accordingly. Will this stand up in court? Maybe, maybe not but, again, they're not looking to get bogged down in arguments they just want to make a quick buck at your expense and as soon as you make it complicated it's starting to cost them money. If they're daft enough to take their chances in court, counterclaim for the charges they've incurred against you.
It can also be worth finding out who the landowner is as a lot of these things happen on retail parks. Big chains - who might have innocently handed a contract to a company years ago to stop people using them as free football parking - HATE the publicity that come with these and in these days of social media it's not hard to stir up some backlash against them. Even though the larger company may have closed the store on the site in question, they may still own the land.
One final point, remember that they can only chance their arm against the registered keeper of the vehicle if they cannot identify the driver of the vehicle at the time, or if the registered keeper is unable or unwilling to identify who was driving at the time. If you (as registered keeper) can supply them with the name and a serviceable address for the person driving at the time, your duty has been discharged. So double-check if your cousin Alan was visiting from India at the time...
some of these companies are design to rack up fines....to cut a story short, did a quick companies house check & popped around the directors house to offer to pay the fine before the price went up anymore. Although after a short discussion the nice chap offered to right it off