I used to live in Europe, I really don't understand why they don't ban plastic bags altogether. Instead we could have cellulose or cassava "plastic" bags instead. Look and feel the same, do everything a plastic carrier can do but fully biodegradable.
Paper bags - like primark - are all well and good for hot, dry countries/areas, not much bloody use here in west Scotland where it rains heavily most of the year!
I remember my mum still mostly using cardboard boxes that the supermarkets would place on shelving across from the tills in the 80's and 90's. Annoying they stopped doing this. Better to get at least one more use out of them before recycling.
And actually carrier bags are the least of it certainly supermarket wise. The amount of packing on products is ludicrous.
We also had a fireplace until mid-80's which as pp said meant some rubbish could be used as fuel.
"Biodegradable bags are still harmful. The plastic has to go somewhere." Erm biodegradable bags AREN'T plastic - that's kinda the point.
Have to admit due to my OCD I do request carrier bags but I reuse as much/many times as possible and return to sainsbury's for recycling too.
When I am going out and about I use fabric reusable bags (hessian etc) and my rucksack for heavier items.
When I had a car, as a result of living in Europe where this was the norm at the time, I used those collapsible crates which just stayed in the car. Did the shopping, shopping went through till and straight back unbagged into trolley and then at the car emptied the shopping from the trolley into the crates. Not sure I'd cope with those now though as my backs buggered!
That it's still prohibitively expensive to buy biodegradable bin bags yet most councils insist the rubbish is bagged before going in the bin (plus if like me your 4 bloody flights up in a flat you need a way to carry the rubbish down) and some won't even let you use the biodegradable bags I think is another big issue.