Here in Australia, most supermarket plastic bags are biodegradable, so by the time they might get blown out to sea, or land in the countryside, they have rotted. The cloth bags from the supermarket cost $1 (50p) so they are quite affordable, plus many organisations give away such bags. I've got a Labour party one, a council one, etc.
In any case, I do most of my supermarket shopping at Aldi, and they don't stock plastic bags: you have to bring your own boxes or bags, buy their cloth bags, or stick the stuff into your car boot unbagged.
I think charging for bags and encouraging shops to give the money to appropriate charities is a good idea. When did we get so disorganised that we can't bring our own bags?