My name is ***** ***** I will try an help you today.
I am sorry you have this problem with the car parking company.
As the car park is no private land, this is a contractual issue and ultimately is your word against theirs.
In the unlikely event you would need to take this claim to court the judge would have to decide on the balance of probabilities which version is preferred.
You have done well to have written to them explaining your case and as you paid you should challenge them to sue you for the alleged balance and you can vigorously defend the claim.
It would be a small claim, so their is no entitlement to costs.
Currently there are 2 parking trade associations, the British Parking Association and the International Parking Community. Each has a Code of Practice that their members are required to abide by, but there is no single set of rules, so motorists are vulnerable to bad private parking practices such as deliberately poor signage and unfair parking fines. Ask them if they are a member of either and complain to the association.
By way of comfort, unfair private parking tickets will be eliminated through the introduction of new rules for private car parks, the Communities Secretary Rt Hon Robert Jenrick MP announced on 31 August 2020.
The government has put forward proposals designed to crack down on rogue car parking firms that will form part of a new Parking Code of Practice and Framework.
The proposals include, a maximum cap for parking fines, a 10-minute grace period before a late fine can be issued and a requirement for parking firms to clearly display pricing and terms and conditions.