Been like that in Northern Ireland for ages now. There are some exceptions tho:
Food - such as take away, where there's a contamination risk. (local chinese has a sign up that they'll have to charge 5p if you want drinks in a bag, food comes with a free bag.
Chemists - they can give a free bag ro maintain confidentiality.
Makes it easier for shoplifter too, as nearly everyone is walking out of the shop with armfuls of stuff, makes them harder to spot.