By way of example, what makes you think you were in a council-run car park as opposed to private?
The ONLY clue is the small logo and words North Ayrshire Council squirrelled away at the top left of the sign.
Why do you think the 'disabled' sign has any unique application as regards the law, every private car park in the land uses them?
On which point, there is a binding Code of Practice for private operators which goes on at length and in detail about entrance signs etc. and bringing to a motorist's attention the conditions of use which apply and the sanctions available to the operator for breaches.
I am not aware of any adjudicator or tribunal which applies lower standards to councils when, in effect, they're operating as simple car park operators NB. which is why VAT is chargeable in all off-street car parks whether private or council because they are not exercising a statutory duty.