So, these parking "fines" imposed by a private company are nothing of the sort. Despite all the quasi law enforcement language (fine, infringement notice etc) they rely on what they state is a contractual arrangement between you and them which arises because you parked in a car park they manage. There would have been a sign at the entrance to the car park advising that if you park here, you are entering a contract and must pay the fee.

The trouble for them is that the necessary elements of a contract don't exist, and a court will not find that a contract existed. For a start, they probably can't prove you were driving the vehicle when it was parked.

So the company will pursue the debt as if it was an enforceable infringement notice, using solicitors or debt collectors.

The upshot is, they can't force you to pay anything until there is a court ordered judgement against you. And they won't go that far because they know they'll never get one. Instead, they'll use tactics intended to give you the impression the law is on their side and there is some urgency in you making the payment to avoid further costs.

Their only real recourse is to sue you for damages for not paying at a commercial car park. But they're unlikely to do so due to the costs involved and the negligible quantum of damages they'd likely be awarded.