In Watching the English, Kate Fox gives a thorough explanation of how much she can pin down someone's social class by what they buy at Marks and Spencers (which is a department store that's branched out into groceries). I forget the exact details, but I think it was that doing a full food shop there made you upper-middle class, buying some food items there made you middle-middle class, and buying food items for special occasions there made you lower-middle class. Buying clothes from M&S makes you middle-middle class, and buying homewares makes you lower-middle class. The upper class don't shop at M&S at all, and the working class only buy clothes or homewares from there if they want something special. (I think - it was a while ago that I read it.) And that's just one shop.
Everywhere does social stratification, but nowhere does it like Britain.
'Watching the English' is nearly 40 years old now and a lot of things have changed. M&S is no longer hugely more expensive than other stores, for food I think Waitrose has taken its place.
Also this article is veering into the idea that class is all about money, which may work in the US but is far from being true in the UK.
There is an updated version by the way. Don't know if that bit has been updated.
I still think doing your whole food shop at M&S is 'higher class' than doing it at Waitrose, but it's weird because of the M&S Simply Food shops which are more geared I think to somebody in a city buying a day or two's food.
And you are right, class is much much more complicated than just money :-)
Everywhere does social stratification, but nowhere does it like Britain.