As far as the law is concerned this is not accurate. The invoice itself is actually invalid, as it has no grounds in law - only in the belief of the company that they can issue tickets in this way.
The reason is that the Car Park itself is private property, and the many tickets appear to 'represent' themselves as being issued under particular Acts of Law, which do not relate to private property.
It is true to say that you may be asked to pay a fee for parking on private property by the owner of the land. He/she may also employ someone to collect that money on his/her behalf. He/she may also pay that person (or company) for doing so. He/she may bank the money so received.
contd