Labour battles the BNP on class and race‏

It says "there has been a renewed recognition of the importance of class", arguing that in schools, for example, "there are greater similarities between black and white children from working class families than between working class and middle class children from the same ethnic group".

Very much so.
I remember attending a Fabian event where there was a fair spread of ethnic minorities. Given the population statistics I would say they were over represented.
Yet me and the mrs were the only ones there from a lower middle-class background. It seemed that everyone else there was pretty posh, public/private/independent school educated, and groomed and bred for power from an early age.
That to me is going to be key in the future. Ethnic divisions of all colours and styles should be properly represented but class is also an issue. Say that parliament was arranged so that it was fully representative along ethnic lines: if that Fabian meeting was a template then the class issue would not be represented as the upper classes would remain over represented even if the ethnicity question was addressed properly.
So yeah, class still matters. More than anything else.