If it was me, I'd fight it; I don't think you're going to succeed in your appeal but if you follow the process all the way up to the PATAS (Parking and Traffic Appeals Service) you'll make the council work for their money. I'm with the first poster; I despise traffic wardens and have no sympathy for the argument that they're just doing their job since they had to apply for it in the first place.
Naturally there should be a system of controlling the way people park their vehicles, but when it's clear, as now, that the infringement is for a lawful activity rather than someone not wanting to walk 50 yards to the shop, there appears to be no room for officer discretion, allowing for the possibility that they would use it,