I would rather appeal using the process first than get into a debate on whether or not their paperwork is compliant as the second route is often long and complicated.
When you look up their evidence on the system you can see they have circled a member of my family walking about in the carpark.
I am still guessing here but I am wondering if "unauthorised parking" means they think the carpark was used to go to another shop or somewhere else other than Wing Yip where the car park is situated. One of them went into the supermarket and the other was roaming about waiting for the shop to be completed.
But it's still a bit of a mystery as "unauthorised parking" says nothing to me.
I'm sorry, but which planet have you just arrived from? No initial appeal, no matter how well formed and logical, will ever be accepted by any unregulated private parking firm. Also, because you are dealing with the bottom-swelling end of the private parking firm spectrum, the odds of a secondary appeal to the kangaroo court that is the IAS is extremely unlikely to be successful either.
You have come here for advice and your first reaction is to suggest that the advice you have received to this point is not correct. You either follow the advice exactly as provided here and you will never pay a penny to UKPS, even is it means that the only route is prolonged although not intensive or you FUBAR it and deal with the consequences.
This location is a very well known money spinner for UKPS. They make a fortune from the majority of the low-hanging fruit on the gullible tree who are easily intimidated into paying out of ignorance and fear. However, from mine and others experience on here, they are easily defeated once they take the process to a county court claim and with our advice, defend it and then it is eventually struck out or discontinued.
However, feel free to try your own way and waste all the time and effort to achieve the exact same ending. I will bet you £100 right now that you will not get this cancelled at any appeal stage. It will only be ended after they go through the intimidation process of making a county court claim and eventually give in just before they have to pay the £27 trial fee, about 4 weeks before the hearing is scheduled at the defendants local county court which would be in around 9-12+ months from now.
This is all about contract law and nothing else. Unless you know how to argue "unauthorised" parking and can evidence the signage that fails to offer any contract with the driver, then good luck and please let us know how you get on.