The crux of the matter is that a fine, handed down by a court, is legally enforceable.
Council run car parks use penalty notices. These too are legally enforceable under whatever bye laws the council has to control parking
However, private companies who operate car parks have no legal powers to force you to pay any penalty they issue. What they are actually sending you is an invoice, which you can either pay or not pay as you wish. The car park operator can take action in a civil court but would have to show consequential loss. If they could prove that your untidy parking deprived them of income from a space next door that could not be used then they might have a case in this instance. But, they would have to prove that to the satisfaction of the court. Given the costs of all this it's unlikely they will do so, particularly if the car park was not full.
So, the threat of fines is all bluff and technically incorrect in this case. If you received one of these penalties and felt it was unfair then you just refuse to pay it and invite them to sue. or you could do, what a number of people have done, is send a token amount for any inconvenience caused.
(IANAL, just curious): Presumably such an invoice could only be issued if an agreement to the price and conditions of a service had been made between the motorist and car park owner? I'm surprised if one can refuse to pay for something simply on the grounds that one finds it unreasonable (and there's no loss to the service provider).
If there is no such agreement made, or in the case of a "no parking" notice, the landowner could sue for trespass - though again they would have to show what the loss to them is.
So it seems someone could park outside my house, or dump a load of rusty old anvils in my garden, and there's nothing I could do?
There is a lot of comment about Private Parking Companies to be found here:-
http://forums.moneysavingexpert.com/forumdisplay.php?f=163