Asda are removing single-use bags from their tills from June. They're under the counter and you have to ask the assistant for one. My local one already has this implemented, with bags for life in the bag rack thing instead, and the cashier keeping an eye and charging for how many you use. Obviously if you take your own bags, nae charge.
Frankly, if Asda can do this (which is one of the cheapest supermarkets out there), why the hell can't Tesco, Sainsbury's, Morrison's etc?
Asda to remove single-use carriers from checkouts - Talking Retail