Their job is to sell food, not to be an environmental consumer service department.
Their job might be to sell food but their responsibility is to their shareholders. I heard Morrisons (I'm not in the UK) have really cut down on their plastic in the fruit & veg department. Enough customers asking why Sainsbury's or Tesco (or any others) aren't doing the same is a perfectly legitimate question.
I use mesh bags for fruit and veg and for the things I want which come in plastic I always mention it at the checkout, then I go to the information and mention it there. Sometimes I'll mail about it to the company HQ and usually I'll tweet.
The result where I live is that people have come up and asked me where I got my bags, shouted across to a partner things like "SEE! it CAN be done!" and finally the store manager came up and said that they were selling those types of bags now and what else did I think they could do, short term, to help with the plastic.
So it does work. And it will work if everyone takes a few small steps in a plastic-reducing direction.
One thing did make me laugh. Got to the checkout with a bagful of loose mushrooms. (Just over 1kg) and the woman at the checkout said "oh no, you've weighed them wrong, they can't cost that much" so I told her I didn't think so. So she ran over to the scales and came back shaking her head "blimey, if you get the pre-packed ones they cost half that"
So that was another email...