I usually shop at Morrison's. I've had the same issue with produce going bad, so I try not to buy anything in packages. Instead I pick out single items - 2 oranges, 4 mushrooms, 2 green peppers, 2 potatoes, 1 aubergine, etc. In the long run, I think it's cheaper than buying a discount bag of something, if you're going to throw away half the bag before you finish it. For leafy greens I might buy a small amount of pak choi or chicory. There's no point in buying a large, full head of cabbage or lettuce.
I tried buying the marked down things in M&S. One day I was in there, and there were tomatoes on sale that were visibly mouldy. The following week, I bought some mincemeat, and when I opened it - two days before the use by date - it smelled and was changing colour. Still later, someone mentioned in a conversation that all of the M&S deals consists of old stuff that they want to get rid of. Since their items that aren't marked down are too expensive for me, I won't be shopping there.