Actually, I think it is you who have not read my posts properly.
Secondly, I have said that by the car staying too long in a parking space, a fine is due on it. That is, according to the parking contract, a fact. Regardless of the reason. It is very simple.
That, I think, is an oversimplification that could have come from a parking company. So, like you, I will play Devil's Advocate with a completely fictitious scenario ...
Alvin has overstayed their allotted time in the airport car park because the runway was closed; the parking company says they should have moved their car by 3pm and they didn't move until 9pm. As a result, Fair Parking Services Ltd had to turn away another gentleman and his booking at a cost of £8/day. They charge Alvin an extra £8 plus admin fee of £5.
This is, I think most people would agree, fair. The cost to the company was about that.
Unfortunately for Brett, his co-flyer, chose to park with Nefarious Parking Services. They charged him, a late fee of £300/day and he has a stonking big bill for the airport closing the runway.
Fair? Of course not.
The small print in any contract doesn't make the illegal, legal or does it make the unfair, fair. In this case, the original poster acted in good faith. They were hypo. DVLA rules state you shouldn't pilot your vehicle for 45 minutes after coming back up and the OP said they were 20 minutes late. So the most the parking company lost was the hourly charge on the car park, £1.50 to get the details from the DVLA and an admin charge. Say, £5.
And the car park operator needs to be a member of the BPA and they are forced to adhere to their code of practice (required to get the details from the DVLA) -
http://www.britishparking.co.uk/write/Documents/AOS_Code_of_Practice_October_2015_update_V6..pdf
POPLA appeal advice is
http://www.parkingcowboys.co.uk/popla/
I had a parking ticket issued by Macclesfield Hospital (it's an infamous, contentious and ridiculous private-parking nightmare). I was late leaving - by two minutes - and was caught by the ANPR. I was treating my daughter's hypo and we had to stop getting to the car as we got the kit out, tested, treated, and then walked slowly back to the vehicle. I got the ticket annulled for that reason. I used the fact that my daughter had a chronic condition, which is a disability and the parking company had to make provisions for people with disabilities to ensure they are not disadvantaged.
Nice letter at first; ticket annulled by return of post.
Good luck