As a kid I distinctly remember a thing called THE shopping bag. Every family had one, and it hung behind the kitchen door. Your mum used to send you to the shops with it, and it always smelled of potatoes.
I used to work for Tescos in the 70s and we used to have a massive pile of boxes, all sizes - leftovers from the shelf stacking- piled against the wall for customers who wanted to pack their groceries into a box before carting them off to their car. There were plastic bags too, but they cost money, and most people opted for the box option.
There were bloody riots if the boxes weren't available, but most people did bring bags of some sort.