Speaking yesterday at the Access on Action conference in London, Alan Milburn said it was time for universities to “grasp the nettle of contextual data” when selecting pupils for admission.

The former health secretary and Labour MP is due to publish a report on social mobility, focusing on higher education, in the spring in his role as the government’s independent reviewer on social mobility and child poverty.

Using information on a candidate’s school and family income was vital to ensure “access to university is genuinely open to the widest possible range of students”, he said

Research also suggested that students from state schools generally performed better than those from private schools if they achieved the same results at A-level, he added.

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“Clearly academic attainment should remain key to a university place,” Mr Milburn said.

“If you can’t do maths at school it’s unlikely you will be able to do it at university. No other single indicator provides better evidence of how a young person will get on at university than their A-level results.

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“But they are not fool-proof in predicting future performance.

“We know from Hefce [the Higher Education Funding Council for England] evidence that a typical state school pupil - once they get in to university - performs at the same or at a higher level than privately educated pupils who have better A-level grades.

“Studies at the University of Bristol and at the University of Oxford have bolstered that evidence base.

“They suggest that a pupil getting good but lower A-level grades from a poorly performing school may do better at university than somebody with better A levels from a high performing school.”

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Mr Milburn said he thought that most people would accept that “a youngster with no family history of going to university from a disadvantaged area, attending a low achieving school, has had to work harder to get decent A-levels than a similar youngster who has attended a top school, having been brought up by well-off parents, who know the university system like the back of their hand”.

Universities were fearful of advancing arguments regarding contextual data after the “media onslaught” against those, such as Bristol, that advocated the approach, he said.

“Universities have to summon up the courage to get out and make a positive argument for change,” he added. “It cannot be done surreptitiously.

“It has to be done openly. It means confronting the argument that greater fairness means lower quality.”

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Institutions that refuse to view social mobility as part of their responsibilities should face financial penalties, he added.

“To those universities I say if you are not prepared to serve the public good, you shouldn’t accept public finance,” he said.

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jack.grove@tsleducation.com