Figures show that, despite the Government's efforts, the proportion of Oxford University students from the lowest socio-economic groups has fallen, from 11.4 per cent to below 10 per cent. So should everyone - ministers, teachers, admissions tutors, even journalists, who bang on about it - give up? Are the workers' children missing out on university places simply because they are thick?
That appears to be the view of Bruce Charlton, an evolutionary psychiatrist at Newcastle University whose paper on class differences in IQ was reported recently in this paper's sister publication, the Times Higher Education. His view is that "higher social classes have a significantly higher average IQ than lower social classes".
As a simple fact, what Dr Charlton says cannot be disputed. Though some high IQs are found among, say, unskilled labourers, we do not expect to find low IQs among doctors. The question is: what conclusions do we draw for their respective offspring?
Dr Charlton implicitly assumes that children's IQ is 100 per cent inherited from their parents. But IQ is a slippery concept. Biologists, psychologists and other specialists have argued over the precise contributions that genes and environment make to scores. Most believe it is the interaction between the two. Genetically well-endowed children tend to attract experiences - through responses of parents and teachers, for example - that further stimulate IQs. The trouble is that, in some environments, even bright children will so lack stimulation that their IQ falls below that of peers who were less brainy at birth.
Leon Feinstein, of London University's Institute of Education, supports this hypothesis. His research, based on the British Cohort Study of more than 17,000 children born in one particular week of April 1970, found that bright children from poor families who did well in tests at 22 months had, on average, fallen back, relative to other children, each time they were tested again - at 42 months, five years and 10 years.
The reverse happened to children from middle-class families who were in the bottom 25 per cent in the first tests. By age 10, they had overtaken the bright lower-class children who had been ahead of them in infancy.
So something in poor homes - parental stress, lack of time, poor housing - depresses the development of bright children. And schools, far from compensating for the deficit, seem to add to it. Or perhaps the slide is so strong that by the time children start, school teachers are powerless to reverse it.
Whatever the explanation, the research makes a nonsense of Dr Charlton's belief that class bias in university admissions can be excused by IQ disparities. IQ - which universities do not measure - is itself at least partially the product of home background. If bright working-class children cannot present themselves to admissions tutors in satisfactory order, that is largely because they live in a society of poverty and inequality.
Universities may reply that this is for politicians to cure. But university education is one of many goods that is unequally distributed, and itself contributes to the persistence of social injustice. The battle must continue.
Peter Wilby is former editor of 'The New Statesman' and 'The Independent on Sunday'.