So is it agreed that the only legislation under which they can issue Parking Charge Notices is the POF Act?
As already mentioned, these are some important facts;
A "PCN" is a name made up by the private parking companies to emulate the "PCN" issued by authorities - You guessed it - of all the acronyms they could have come up with they came up with the exactly that of the 'official' Penalty Charge Notice.
And guess what, they also use the same yellow square design as well!
I'm pretty sure that the term "Parking Charge Notice" is never mentioned in any legislation.
A PCN is nothing more than a 'speculative invoice' in legal terms.
Of course, they present it like some kind of formal (official) document.
This is a numbers game and their sole aim is to convince as many people as possible to pay the charge (hence its wording / design etc already mentioned).
When the PCN is first issued, although the invoice is addressed to the keeper, the liability in law remains solely with the driver - liability remains with the driver for just over 28 days.
POFA only comes into the equation after the 28 day period but the PCN should be set out in a certain manner to ensure POFA compliance should the need arise.
There is no requirement that a parking operator must use POFA.
If they wanted they could just send an invoice which says, "Oi, the driver of your motor owes us £60 because your car was parked in our car park last week and you never paid nuffing"
Of course, if you refused to pay the invoice then there would be nothing they could do because such an invoice would not be POFA compliant and the liability could never be moved from the unknown driver onto the known keeper.
So, in terms of your question;
They can issue a speculative invoice (PCN) for any reason they want and the issuing of such an invoice is based totally in contract law and not in any other specific legislation.
POFA only comes in after 28 days+ in the instance that there is no payment and no other driver is nominated to the parking operator.