An update: I went upto Asda this morning as soon as it opened, and went straight to Customer Services and asked to see the Store Manager (and named him). They said he was out today, but his assistant would come down. I had the original PCN, a photocopy to give them, and a printout of the list of purchases I'd made at Asda in the last 2 months... it was a significant amount!
I explained the situation - that I'd left the car park at 9am, been at work most of the day when they claimed I was in the Asda Car Park, and then returned after 1630...and that we were regular customers (showing