I'm not sure how the conclusion that "this has never been tested in court" has been arrived at.
Firstly, most elements of most civil litigation are not a matter of public record in the UK and not all cases are reported. Even an exhaustive search of law reports and litigation databases (which would take a trained person with access hours if not days) that failed to identify any such cases couldn't show that there had never been such a case. The only people who have an accurate idea on how often these claims are litigated are the parking companies themselves.
Secondly, the principle of contractual terms incorporated by way of signage has been discussed in court a billion zillion times since the late 19th century. One of the leading cases in English law is Shoe Lane Parking which iirc is about incorporation of a term limiting liability in the event of a car park user's personal injury. (A topic close to a certain STWer's heart, istr).
I also find it quite interesting that the case you suggest I look at concerns a company trying to enforce something which would be illegal under current law!
Then you didn't understand the case or how to read cases.
Dunlop's five pound liquidated damages term was unreasonable in the circumstances of that contract, as a question of fact. This does not mean that any liquidated damages term in the contract would have been unenforceable. In fact, Dunlop stands for the principle that "it seems quite reasonable for parties to contract that they should estimate that damage at a certain figure, and provided that figure is not extravagant there would seem no reason to suspect that it is not truly a bargain to assess damages, but rather a penalty to be held in terrorem."
The fact that price fixing and resale price maintenance are (generally) now prohibited by statute is irrelevant.
"It will be held to be penalty if the sum stipulated for is extravagant and unconscionable in amount in comparison with the greatest loss that could conceivably be proved to have followed from the breach" which is quite clearly the case for a £50 penalty relating to not paying £2 for parking. That quote from somebody with rather greater legal knowledge than you makes it clear that "Liquidated damages don't have to be based on actual loss in a particular circumstance" is a complete load of rubbish - to be legally enforceable, liquidated damages do very much have to be based on the loss incurred, using them as a penalty (which is what you seem to be implying) isn't legally allowable."
You are simply making an unsustainable leap here. First, you are failing to consider that lost revenue from parking is not the only or greatest loss that could follow from breach of the contract. Second, you are assuming that all parking-related liquidated damages claims are unreasonable per se and therefore unenforceable - but that is not true because it depends on each individual circumstance.
If (as you argue) a claim for liquidated damages can only based on actual loss, then there is simply no role for liquidated damages as a concept because the loss of each breach will have to be assessed on a case-by-case basis. The entire point of liquidated damages is to avoid that situation. Again, from Dunlop:
"In Kemble v. Farren(1) Tindal C.J. said: "We see nothing illegal or unreasonable in the parties, by their mutual agreement, settling the amount of damages, uncertain in their nature, at any sum upon which they may agree. In many cases, such an agreement fixes that which is almost impossible to be accurately ascertained; and in all cases, it saves the expense and difficulty of bringing witnesses to that point.""
On a practical level, I would probably ignore the letters for a fair while if I got one. It doesn't seem that the companies are actually interesting in litigating anything and it's cheaper/easier for them to send out more letters to more people than it is to sue.
Anyway, as much fun as this has been...
