Not until after they've been stopped by Security and accused of shoplifting three times because they don't have a Primark bag, at any rate.
The argument we used to have for charging for paper bags was that they cost more to produce in terms of money and energy than plastic, but then they were cheaper because they were potentially biodegradable/wouldn't be around for five thousand years choking turtles.
I miss the decent hessian bags more. Managed to get a couple recently that were so small in comparison, but the previous ones lasted about 15 years.