The fact that Canterbury is a city with very limited space means it has a very unusual set up when it comes to supermarkets! The town centre of Canterbury is squashed into its city walls. The wierdest thing I find about Canterbury is that it has no tesco superstore, and its a city, now that is strange. Canterbury does however have a small Tesco within its city walls. The Tesco is a Tesco Metro and although small will cater for general tastes and you can get most things you would need there during the week, it's variety is obviously limited due to the size and the more obscure things cannot be found there. Without meaning to state the obvious, the extras that Tesco has become more famous for (opticians, clothes, pharmacy etc) cannot be found there. You cannot park there, although you can park nearby, so this is another reson that may discourage people from doing a longer shop.
Still within Canterbury city, yet just outside the city centre are more supermarkets. There is a bigger Asda with ample car parking. There is also a nettos, lidl and Morrisons. Morrisons is the closest to the city centre and parking is free if you spend over a certain amount (ten pounds I believe) on your shopping.