Aldi use ParkingEye in the majority of their stores and have a "genuine customer" clause in their arrangements with ParkingEye. Here is a typical response.
Thank you for your recent email concerning the parking charge notice you received.
As you have used the store on the day I am confident we can assist with your appeal. However, to do this we would require a proof of purchase (either a receipt for your shopping or a bank statement for a debit card transaction).
As you no longer have your receipt and paid for your shopping in cash, please return to the store and speak to the store manager, they will be able to locate a copy of your receipt. To enable them to do this they will require an approximate transaction total and a few items that were purchased. You will of course know the approximate transaction time from the parking charge notice that you received.
If you would like our assistance with your appeal then please post a copy of your receipt or bank statement along with your parking charge details to the below address. If you would prefer to appeal online please follow the appeal process on the reverse of the charge.
ALDI Stores Ltd
Aldi Parking Management
Aldi Customer Services
UK: 0800 042 0800 FREE