From the council's website:
Where you can park
Whilst displaying a care and health worker permit, you may use your permit to park for free and for as long as your client’s or patient’s scheduled visit lasts (up to three hours) when:
parked on street in areas of limited waiting
parked on street in resident permit holder bays
using on street pay and display spaces (but not car parks)
using any combination of the above
You may also use it to park for up to three hours on most single or double yellow lines if all the parking spaces on the street are taken, or none exist near your client’s address.
From this it would seem that the burden lies with you here i.e. to convince the authority that when you parked 'all the parking spaces on the street are taken, or none exist near your client’s address'.
As the PCN was issued so soon after you parked, any adjudicator would take the photos of the surrounding area as representing the situation when you parked.
EDIT - IMO, you should think about what the CEO saw when they issued the PCN i.e. they saw the car in a road context. They knew nothing about shopping or whatever, so I wouldn't even go there. IMO, they MUST presume legitimate use if the permit is displayed correctly. But whether legitimate use = no contravention depends upon the prevailing circumstances which are whether 'if all the parking spaces on the street are taken, or none exist near your client’s address'. Of these, only the use of the road would be evident to the CEO.
I can't see your photos so, do any show free parking spaces in the vicinity of your car. IMO, even in this respect, 'vicinity' is subjective and as the client's incapacity would not be known to the CEO, then either there were free spaces very near or, IMO more likely, the CEO did not understand the use of your permit! In which case, IMO don't go beyond the basic and obvious in informal reps.
