This is a company called " Parking Eye". They use a number plate recognition systen to capture your car details and trace you home address.
If you were genuinely in the shop for that time, then go and see the manager of the shop. Explain to him the fine and that his actions in dealing with the matter (ie. tearing up the fine or not) will affect your future choice of supermarket. I would reckon it depends on the time given on your till receipt (if Aldi do have time and date stamped receipts).
If he fails to budge, don't shop there again or phone or write a letter to head office and explain. I don't see why they shouldn't take back the fine and have a word with the company.
This method of parking seems completely mad and allows for no movement. I don't see why there isn't a £2 charge for 2 hours, refundable at the shop when you go to the checkout.
Have a look at this site for moterists, it should give you some advice:
http://www.pepipoo.com/
EDIT: Oh, and if you want to write directly to the parking company to appeal, here is the address:To appeal against your Parking Charge, write to ParkingEye at PO Box 565, Chorley, PR6 6HT, giving your reason for the appeal and enclosing any supporting information you may have, ie a receipt to prove expenditure at the location, a P&D ticket, etc.