Jeremy- I think you're wrong about tax credits causing this. (Though I admit it may have amplified an already existing issue). I went to school before tax credits. There was family allowance, and there were FSM also, but that was it. I went to a (really quite poor) state school that was ex-secondary modern, but grammars had been axed in our LEA. It was approx 50% white British, and 50% British Asian (the majority of whom were second or third generation immigrants from Pakistan and Bangladesh).
In school 95% of the Asian origin children worked hard. Many of them were v low achievers, possibly due to language issues, (all but two of my friends spoke a community language at home, not English) or undiagnosed additional needs, but they worked hard, did their homework, tried in all assignments etc. They were destined for factory jobs, a few for construction, and the girls for marriage/children. They knew that in Y7, and they used school to gain as much knowledge and understanding of the world before going on to what had been determined for them by their parents. They had respect for the staff, in the main.
Of the white children (99% of whom were traditional working class), probably 40% of them worked hard, tried their best, some did well in their new fangled GCSEs, most did not. After school some went to college (mainly day releases, doing hair and beauty or car mechanics), some went into retail, or into family businesses such as carpentry and painting & decorating. Of the other 60%, most were aiming for a life on unemployment benefit, several girls were already up-duffed on leaving, so they could get a flat 'like my sister has' when the baby arrived. Many were from workless families, they were the third generation that were going to be workless, and they weren't worried about that, nor ashamed, it was simply a fact of life. Some were from single-parent families, but in truth most of the children from single-parent families worked their socks off because they saw how hard their mums had it.
This was long before tax credits, and when Gordon Brown had only just entered parliament, let alone the shadow cabinet.
I think the clearances of the slums after the second world war (a good thing, surely!) and the building of new council homes destroyed the old WC communities. That coupled with the decline and loss of their industries, and the introduction of the welfare state have meant that as a whole they have given up on life, given up toiling (I mean, where did it get them? Look what happened to their industries, manufacturing was no longer respected as a good honest living, trade and artisanship no longer valued because modern things were desirable, all made in a factory in China.)
The white children in this study aren't WC, because there isn't a WC really any more. They're seen as underclass, they're certainly the class 'at the bottom', and they're not respected, nor valued, or given any meaningful purpose or role in society. So why would they bother? And why would their parents value education, or push them to do well at it? It doesn't get you anywhere.
In 21st century Britain, you need a worthless degree to do a job 14/15 yo school leavers would have done forty years ago, or jobs that hadn't been invented then, purely in existence to service a society that produces nothing, yet needs to occupy all.
Good lord, that was depressing.