I remember reading on another forum, co-incidentally a private firm operating a car park for Asda a similar thing, basically they refused to pay the fine, the firm kept sending ever increasing demands, then started to decrease again, then the car park firm gave up chasing. You have to be prepared to stand your ground which they know most people won't.
it's only if an official law enforcement agency or 3rd party on their behalf contacts you then you have to pay, e.g. council run car park.
I'm not a lawyer though, so this may be out of date info, google, watchdog, mse can probably help with concrete advise rather than hearsay
Good luck.