If you get a private one, the best cause of action is to offer a payment equivalent to what they'd normally charge for the amount of time you'd spent in the car park. If you have offered this and they then refuse it and take you to court, you then have evidence that you have tried to cover the cost to them that they could have incured by you car taking the space of another paying customer.
Also, It's not a "fine", private car park operators are not allowed to fine you, and if they use that word in any documentation relating to a charge they want you to pay they are breaking the law. The c