I was wondering about this earlier, as I headed to the allotment. Until now, I've used many-times-recycled carrier bags to bring home mud-covered veg. Right now, I'm having to resort to using sandwich bags for some of them, and in very large quantities. Then I have to throw them away, because the majority aren't fit to use again. Personally, I am likely to be producing far more plastic waste now than I did before unless I find a more environmentally friendly (but cheap and convenient) way of transporting them!
Also, there was the plastic bag that I tie around the end of the strimmer so it didn't cover the car in mud and grass. I suppose that when the current one falls apart, I will have to use dustbin bags instead!
I wonder, in the places where free bags were outlawed before ours, has there been any monitoring of sales of other types of plastic bags such as bin liners to see if they have risen? It would be interesting to know.