5p isn't going to change anyones behaviour. Make it a proper tax where every bag costs £1 and the supermarket has to give it directly to the chancellor, no profiteering. If people knew they were paying into the government's coffers, that would encorage 'em to bring a bag with them.
As Mikey says, it works here in Wales, we are just used to it now, everyone tends to carry bags with them or have them in the car ready for the shopping, as for not having the carrier bags to use as rubbish bags, I use the endless amount of charity bags in my swing bin, we get two to three put through our door every week, and every week I leave the unused ones out to be collected to be re-used, they never get collected, and end up as bin bags. re-cycling of a sort I suppose.