The independent fishmonger etc. is a lovely thought, but currently rather impractical.
I'm a pretty middle class guy, I make most of our meals myself, from scratch. I rarely visit a local fishmonger, butcher or baker or whatever for one simple reason - I work. Almost all of the lovely local shops are only open during the working day, when I'm not around. I do a certain amount at the weekend, but that can only get you so far.
Our local supermarkets may not carry a massively exciting range of fish or meat - though they're not bad - but at least they are open when I have the option of shopping.
There are other options that could make all this work - but they will take time to fit in, you're talking about pretty fundamental cultural and economic changes.