I don’t think there’s a simple answer to this question.
If you’ve parked in a private car park, you have to check their rules.
If you park in a council car park, you have to check their rules too. For eg, the council area I live in, I can park in any space in any car park, display my badge and not have to pay. But in the neighbouring Borough, I can park for free only in a space that is designated for the disabled. Equally, parking on a meter depends on the councils’ rules.
If I park in an NCP car park, it’s never free, regardless of where I park, ie. its a privately owned car park with specific rules.
The only rules that are (I think) common to the whole country are those about parking on single or double yellow lines (up to 3 hours displaying a badge and time clock so long as it’s safe and there are no restrictions). And of course if you live in an area where there are red lines, it’s never OK to park.
So you’d need to check the rules of the specific private car park you were in.
But you could try appealing anyway, it’s always worth a try.