Conor Ryan on the implications of today’s teacher polling.

What are we to make of the idea that some four in ten teachers rarely or never advise bright students to apply to Oxford and Cambridge? This finding in an NFER poll for the Sutton Trust published today has remained stubbornly unchanged since 2007.

And perhaps more troubling is the perception that teachers have of the proportions of undergraduates at our two most prestigious universities who come from state schools  – typically they say 20%, around a third of the actual percentage.

There is no doubt that there is still a real access issue at our best universities. At the top third, you are six times more likely to gain admittance if you come from the richest fifth of neighbourhoods than if you live in the poorest fifth. At our most selective universities, the odds are even lower. Yet the universities spend millions of pounds each year on outreach, and lots more on bursaries, designed to narrow these gaps.

It is good that Oxford now has 59% of students from a state school background, and Cambridge has slightly more. That’s a real improvement, but it still means that taking into account sixth form attendance, privately educated students are three times more likely to gain a place than their numbers in the population.

The Russell Group always argue the answer is attainment: A-levels achieved by those in the leafier communities outweigh those from the less advantaged by a significant margin at the top. Yet that’s not the whole story. The Sutton Trust identified a ‘missing 3000’ some years ago who make the grades but don’t get in to the top 13 universities. There is little sign that has changed.

And they’re the group who may lose out if teachers don’t encourage their brightest students to apply to Oxford and Cambridge, and other leading universities. Both universities are central to the leading professions and best salaries, and if we are to make a difference to social mobility at the top we need to see more young people of real ability from low and middle income homes getting to those great universities.

This isn’t about criticising teachers or Oxbridge dons. It is about both schools and the colleges and universities being prepared to look afresh at how they work and being open to making the changes that could break down these barriers.

Earlier this year, the Trust published a brief on admissions procedures at the two universities and made some fairly practical suggestions based on what state school headteachers with a track record of success at the universities, and some of the alumni from our summer schools had said to us.

University rather than college-based admissions are more common, but the distinctions that remain are more of a hindrance to state students than those from private schools with the right networks. What contextual admission offers that are made remain opaque and the information about bursaries and other financial aid is simply not known by too many schools. With a new VC at Oxford showing a strong commitment to fair access and change coming at Cambridge there is a real opportunity for a radical fresh look at what could make a difference.

But equally, schools need to do far more to stretch their highly able students. Grammar schools still have disproportionate Oxbridge entries compared to their numbers too. Every comprehensive should have a strong programme of enrichment for their brightest students from early on in their secondary education. The Sutton Trust works with students to provide such stretch through its Sutton Scholars programme, but programmes for what schools call the able, gifted and talented need to be as embedded in the culture of every comprehensive as much as their support for those with special educational needs.

Our Missing Talent report last year showed what happens where schools don’t do this: we identified thousands of students in the top 10 per cent at age 11 who had fallen outside the top 25 per cent by the age of 16. They could have been set fair for top universities, but had lost that chance. That’s why we need the government not only to require grammars to do much more to recruit bright disadvantaged pupils, we need them to be clear that this should be a part of the DNA of every comprehensive too. To his credit, Sir Michael Wilshaw has pushed this agenda in his time as chief inspector. But this needs drive from the whole government and as much focus as the Prime Minister has given to grammars and faith schools.

Of course, many schools and sixth form colleges do push their best students to aim high, and universities do run more programmes than ever to reach them. But today’s research shows that this needs to be a national drive if we are to make a real difference to social mobility at the top.