The Prime Minister and his deputy have got themselves into deep water by repeating claims about the admissions policy at Oxford University.
 
David Cameron claimed, wrongly, that only one black student had been admitted to Oxford last year. What he meant to say was one Black Caribbean student. I have written about this at length before, so won’t repeat it. 
 
Nick Clegg then suggested that universities would lose government funding unless their entry better reflected the social mix of British society.
 
He told Sky News: “We do need to make real efforts to say to universities ‘if you want to continue to get support from the taxpayer to educate our young people, you have got to make sure that British society is better reflected in the people you take into the university in the first place’”.
 
He supported his position by arguing that only 40 children who had been on free school meals got places at Oxford and Cambridge last year. This claim appears to be based on the foreword to the 2010 Schools White Paper, in which Education Secretary Michael Gove wrote that in the last year for which we have figures, “just 40 of the 80,000 eligible for free school meals made it to Oxbridge”.
 
Mr Gove did not give a source for this figure but it appears to be an updated version of the figure for the previous year (45) which emerged as a parliamentary answer he asked on 5 February 2010. The then-minister of state, David Lammy, replied by producing estimates based on matching data from the National Pupil Database, the Higher Education Statistics Agency Student Record and the Learning and Skills Council Individualised Learner Record.
 
This produced figures, rounded to the nearest five, of 45 such children winning places at Oxford and Cambridge in 2006-07. I assume, in the absence of other evidence, that the 40 figure quoted by Mr Gove refers to 2007-08. These are not published statistics, as far as I can ascertain.
 
Mr Gove is wrong in at least one particular. The data originally produced in response to his parliamentary question was about pupils “in receipt” of free school meals, not those eligible for them. The two are not the same. We do not know precisely how many children are “eligible” for free school meals, only those that actually claim them. To put it more exactly, FSM status measures the numbers of those who are both “eligible for and claiming” free school meals.
 
Some children whose parental income should entitle them to free school meals do not get them – either because they are not eligible by virtue of the schools they attend (those in sixth-form colleges, further education institutions, or independent schools on bursaries do not qualify), or because their parents do not choose to apply because of social stigma.  
 
Parents can claim FSM if they receive any of:  Income Support, Income-Based Job Seeker’s Allowance, Income-Related Employment and Support Allowance, Child Tax Credit but not Working Tax Credit and the household income is not more than £16,190, the Guarantee element of State Pension Credit, or support under part IV of the Immigration and Asylum Act 1999.
 
In short, getting FSM depends on getting other benefits, and not earning more than £16,190. A study for the DCMS (as it then was) in 2007 found that FSM status proxies most accurately those households with incomes of less than £10,000 a year. But the authors, Graham Hobbs and Anna Vignoles, found it to be an imperfect proxy, both for low-income and for socio-economic status.
 
Free school meals cannot, therefore be claimed simply because parents are poor. They must be poor and in receipt of benefits. Nobody, say Hobbs and Vignoles, has ever studied what proportion of children who are eligible for FSM actually claim them.
 
Oxford has calculated how many of its students come from families with incomes under £16,190, the upper limit for making a claim for free school meals. In the most recent undergraduate entry, 9 per cent come from families with incomes below this level, according to a spokeswoman for the university. A recent letter to The Guardian from the Director of Undergraduate Admissions made the same point. 
 
A household income of under £16,190 includes a lot of people - nearly 40 per cent of all families have disposable incomes lower than this in 2008-09. (See Table below.)  Disposable income is the critical line here: final income includes benefits such as the NHS.
 

 
So 9 per cent of Oxford undergraduates come from (roughly) the poorest 40 per cent of families. Oxford further says that a further13.5 per cent come from households with incomes below £25,000 pa, which includes roughly the lowest 60 per cent of incomes nationally.
 
While these figures certainly give a better impression than the 40 Oxbridge students who had been on free school meals, they do show a large gap in entry between the rich and the poor. This is not, however, the result of prejudice but of differential educational attainment in schools.
 
Of those in receipt of free school meals, around 80,000 pupils, only 5,000 took A levels. And of the 30,000 pupils who gained three A level passes at A grade, the minimum needed for Oxford and Cambridge, just 176 were getting free school meals. If we accept that FSM is a reasonable proxy for incomes of £10,000 a year or less, then very few of the poorest come close to meeting Oxbridge entry  requirements.
 
This is indeed something of a scandal, but the universities are the wrong people to blame. It is the schools that are the engines of social mobility, as Mr Gove indeed remarked in his foreword to the White Paper.
 
"But, at the moment, our schools system does not close gaps, it widens them" he wrote. "Children from poorer homes start behind their wealthier contemporaries when they arrive at school and during their educational journey they fall further and further back.
 
"The achievement gap between rich and poor widens at the beginning of primary school, gets worse by GCSE and is a yawning gulf by the time (far too few) sit A levels and apply to university."
 
 Perhaps he should have a word with Mr Clegg.