Do you remember why you got into education? Like most of us working in schools and universities, my schedule normally gives me few opportunities to reflect on such things. But my work leading the higher education strand for the Prime Minister’s National Council for Educational Excellence (NCEE) has given me a chance to think about this question.

For me, education is fundamental in a changing society. It transforms lives. It makes us different people.

I was the first in my family to go to university. I have never forgotten that. Nor have I forgotten my German teacher at grammar school, who told my parents that the best job I could expect to get was to sweep the floors in the Norvic shoe factory in Norwich.

Thanks to my parents, and to one teacher in particular, Mr Shearing (I never knew your first name and never thanked you), I got the encouragement I needed to raise my aspirations.

Not many people of my social class went to university, and not a day goes by without me reminding myself of how lucky I was. Thus, my job, my commitment, has been to help create the same possibilities for others.

Sadly, I have to acknowledge that social mobility has, if anything, narrowed, not widened, in the UK in the past 30 years. You are much more likely to get a degree if you are from the higher socio-economic groups. In 1948, the probability of going to university for the top two social classes was 78 per cent; in 2005, it was 78 per cent. For the bottom social class it was 14 per cent in 1948, and in 2005 it was 13 per cent. In this context, very little has changed over the past 60 years.

We live in a society where the best predictor of A-level grades is not your educational ability or potential, but your social class. If you are in the top 20 per cent of ability at age 11 and in the three lowest social classes, you stand only a 34 per cent chance of still being in that top ability group at 14, while your chance would be doubled if you were in the top three social classes. It is a society where, in 2006, only 820 students from the lowest social class got three As at A-level.

If we are going to alter this social immobility, everyone in the education system must work together to find new solutions. It is time for universities and schools to be more ambitious.

The widening participation agenda has been with us for many years. It is about getting more pupils from lower socio-economic groups to go on to higher education and reversing this appalling trend of children from the lower classes being massively under-represented in universities.

A subset of this issue is “fair access” - the percentage of pupils that go on to the most selective institutions and the most selective courses. Fair access has dominated the headlines, but it is on widening participation that we should focus our efforts. And higher education institutions, together with schools and colleges, have long been committed to this agenda, working to ensure that students with potential have the chance to take their education to the level they want.

The NCEE, set up by the Prime Minister in 2007, has developed new proposals and initiatives to tackle this problem. I was a member of the council and helped formulate its recommendations, which have now been accepted by government.

Some were aimed at schools. We think aspiration-raising should start at primary school and that older pupils, especially those in more deprived areas, should have the chance to visit a university campus. This may seem a surprising proposal, but evidence shows that educational aspirations are set at a very early age. I know of one senior colleague who was told at primary school that he was “university material” and he clung on to that idea throughout his education.

We thought there should be specific measures to strengthen STEM (science, technology, engineering and maths) in schools. After years in the doldrums, university applications for these subjects are making a comeback, but we still need to do more to encourage able students to take them up.

Linked to our thoughts on primaries, we felt guidance for young people on their careers needed to be redesigned so advice was more timely and children received it from an earlier age. We also felt Ofsted inspectors should play a role in assessing the strength of that guidance.

If we are to widen participation, a joint effort is needed between schools and higher education. I strongly believe there is a key role for universities in supporting schools through providing aspiration-raising activities, information, guidance, and continuing professional development for teachers, but also via formal partnerships with schools, including giving official backing to those that want to become trusts and academies.

We also had many specific recommendations for universities, which will affect the way they treat school-leavers. We want to make sure that university admissions policies are transparent, and have recommended they use contextual information about students’ achievements. All universities should produce comprehensive strategies for their widening participation work and should not use predictions about the new A* at A-level to make offers.

A working party - the Ambassador Group - has spent the past nine months assessing the progress of the main government departments (for Children, Schools and FamiliesInnovation, Universities and Skills) in implementing the recommendations. Real progress has been made, but the political truth is that this progress will take a long time to change the existing patterns of social mobility; crucially, that time-frame does not fit the political cycle.

These are big issues for all of us. Certainly, it is not for universities to pretend from on high that they have all the answers: along with schools and parents, they have to be part of the solution. For this country to be one of social mobility and fairness, we absolutely have to alter the class-based aspiration and achievement patterns of the under-16s. I believe the role of universities and schools in this process will be pivotal.

Professor Steve Smith, Vice-chancellor, Exeter University.