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Update, the registered keeper has received a one line response today stating the PCN has been cancelled.
Thanks to all those above who responded

Yes my partner is the RK.
Thank you for taking the time to review my post. I will use your template, and will post any update/response here.

Hope this works. Pic of front and back of PCN with personal info removed

https://imgur.com/0N5PEwZ
https://imgur.com/ThXZcxx

My partner has received a PCN for "Failure to pay for the duration of the stay" at the above car park, but I categorically remembering paying by cash at the machine, as I had to borrow some coins from my kids. Its a £100 fine, reduced to £60 if I pay in 14 days.

This private car park is situated directly next to Wildhearts Animal Sanctuary, which we were visting that day.
The signage stated that parking costs £3 all day for Sanctuary visitors. Please ensure that you enter the code shown at the top of the parking sign to secure this discounted price.
I distinctly remember doing this when paying the £3 in coins, and putting the ticket in the windscreen. I even confirmed with the Sanctuary staff that I had followed the process correctly.

Unfortunately I cannot find any image on Google maps that shows the signage and code, and of course I no longer have the paper ticket.

Note that this is the car park directly next to the sanctuary, and NOT the tarmac car park on the seafront.

Is there any way I can prove that payment was made, as obviously there is no cash paper trail? On my appeal I am tempted to ask them to provide a reconciliation of all the cash payments taken against numberplates that contain the sanctuary code, but I'll doubt they'll bother with that.

Also I'm not sure if this matters, but the PCN is dated 35 days after the date we were there.

Any assistance greatly appreciated