My experience of local convenience stores is that the fresh fruit & veg often isn't, they just don't have enough turnover to keep the stock shifting before it goes off. That said, since Brexit, even in large supermarkets it's often the case that fresh produce is already going off before it gets on the shelf.
its as fresh as it was in my grandparents day when they had local greengrocers and things, so for sure I bet there are places that push the dates on things now because of low turnover, but I dont shop in those places.
for me the worst culprits are supermarkets ever since they dropped that requirement for best before dates,and its not because of Brexit,but they are selling you stuff thats got a 2-3 day shelf life left, instead of a week or two as it was before.
but again you adapt right, I remember back when fridges were a novelty, and small, my grandparents would shop nearly every other day for fresh produce. they didnt buy stuff to last for the next month, they bought when they needed i.