Drugstore and Healthfoods at 17, Highbury Park, London, N5 2AB (aka Natural Food Store and Fiveboys) is leading the way making Highbury Barn plastic bag free. Since 1 June 2009 the store charges 5p for plastic bags. It also sells compostable bags and partially compostable nappies.
Tip: If you've got a lot of shopping to carry (or heavy stuff like tins) then bring a couple of cloth bags or consider getting a trolley on wheels that looks a bit like a golf cart. There's plenty of room on the buses for them.