Mr Kay went to the car park in Copeland Street on 13 October 2023, when he dropped off his son at a children's party at Jumpin Fun.
He entered the car park at 16:14 BST and said he had to "wait for ages" to get a parking space because the car park was so busy.
He initially did not realise he had to pay, he said, but when he entered Jumpin Fun a member of staff told him he needed to.
He then went outside and bought a £2 ticket for two hours of parking.
By the time Mr Kay got a ticket it was 16:34, because he said there was a queue at the parking machine.
He then decided to stay to watch his son, and eventually left the car park at 17:35, meaning he had been in the car park for one hour and 21 minutes.
Mr Kay later received a PCN asking him to pay £100, reduced to £60 if he paid within 14 days.
The letter said this was because he had failed to purchase the ticket "within the time allowed".
He attempted to appeal the PCN directly with Excel Parking but the company wrote back saying "we are unable to accept your appeal".
It later filed a court claim for "breaching the terms and conditions set on private land".
Although the PCN was £100, Excel Parking added "contractual costs", interest, a court fee and "legal representative's costs", making a total of £255.