Graham Scambler has posted a thoughtful piece on class and the GBCS on the Cost Of Living blog. He argues in favour of a Marx inspired understanding of the notion.
It seems to me that we will just go around in circles having scientifically fruitless, though potentially CV filling, "debates" about what X or Y really is unless the penny drops that we need to specify what we intend to use X or Y for. Concepts are tools and all tools involve trade-offs - they are better at some jobs than others. That implies that choices have to be made and we have to evaluate those choices in terms of their consequences for our goal. It also implies that blanket arguments along the lines of "that leaves so much out", though they may lead to nods of approval from the groupies, just won't do.
Take for instance Marx. If we are going to base our ideas about class on his, which are we going to choose? Are we going to go with the wage-labourers, capitalists and landlords of Capital vol III? Or what about the "lower strata of the middle class - the small tradespeople, shopkeepers...retired tradesmen, the handicraftsmen and peasants..." of the Communist Manifesto. And how about the various class groupings and factions identified in the 18th Brumaire and the Civil War in France? Marx talked about class in different ways for different purposes. In one way when he was writing about an abstract model of political economy and in quite another way when he was writing about politics and history. So why take on one set of ideas rather than another? Choices have to be made and justified in terms of intentions.
It's largely forgotten that the first serious attempt to study social mobility in the the UK - David Glass' Social Mobility in Britain - had as its starting point a focus on : "...the formation and structure of the 'middle classes'.". It is a quirk of intellectual history that Glass, who called himself a Marxist, in practice worked with the notion of the social status of occupations. Why exactly he did this is not clear, but one can conjecture a pragmatic reason - the obvious need in a study of mass social mobility to distinguish between different types of wage-labourer. From the point of view of their social mobility chances not all wage-labourers are the same and it won't be terribly enlightening to treat them as such.
I'm not seeking to defend the particular choices that Glass and his colleagues made. But it is important to point out that criticisms of those choices would be nothing more than cheap talk if they did not seriously engage with why the choices were made in the first place.