Last time I got a 'fine' from a private car park I ignored it. I got lots of letters which got progressively nastier and from progressively more scumbag-sounding entities, but in the end they stopped.
I have had a fine from a council car park though, similar to someone above, I had a permit and it blew off one day. Their letter said their database of exempt cars didn't list me so I had to show the permit, eventhough my car was obviously in the OTHER database of people with a permit. Idiots but for £35 it's impossible to argue with a bureaucrat. A friend got a council PCN because a police car boxed him into a space. Even with a written transcript from the police and their evidence, the council wouldn't budge.
The mistake is assuming anyone who works in these industries is rational, unfortunately I expect they have to enforce their rules as written otherwise their jobs would probably be even worse than they already are. I'm sure they also deal with plenty of people wilfully breaking the rules and trying to get out of paying.