If more than two-thirds of young women now go to university, does that mean it's because they've elbowed young men out of the way to get there, or because they've been champing at the bit for generations? David Willetts, the higher education minister, believes it's because most of the increase in university attendance under the last government benefited middle-class women over working-class men. This may explain his enthusiasm for apprenticeships and technical degrees: got to give those sons of toil something to do, eh?

The social geographer Danny Dorling disagrees, and has evidence to prove it. His new book, Fair Play, shows that in Labour's final term the number of working-class students in higher education began to increase at a faster rate than those from middle-class backgrounds. The increase followed sustained investment in schools and pupils, in particular those who qualified for free school meals and so for the education maintenance allowance.

The beauty of Dorling's figures is that they prove investing in people works. Yet for every Willetts on the right, there is a figure on the left to remind us that social mobility, like meritocracy, is a fallacy – because the supply of jobs at the top is limited, meaning a "less able" person of privilege will always have to move out of the way in order for a "bright" working-class person to progress. Because privilege tends to accumulate over time, that's unlikely to happen without coercion.

Research conducted by the Resolution Foundation, and endorsed by Willetts, shows that the importance of having a degree has increased over time, in defiance of the assumption that the more highly educated people there are, the less valuable their qualifications. In the noughties, the fewer qualifications you had, the harder it was to maintain good earnings. Higher education improves your chances of finding a remunerative, enjoyable line of work.

In 2009, the million+ consortium of new universities reported that, while only 8% of students at its 28 member institutions came from professional families, 17% of students had found professional jobs three years after graduating. That's not enough, of course; but during that decade of expansion, a million public-sector jobs were created, most of them white collar; in the private sector, the creative, financial and legal sectors grew with the number of places on courses in law, media and business.

We can snark all we like about the trend towards job-focused degrees; higher education suffered as much as benefited from New Labour's often depressing instrumentalism. But the point is that they do, in the main, lead to more good jobs: skilled, permanent, relatively well paid, and with room for further advancement. It suggested that social mobility was neither a myth nor an impossibility, and that it was possible to create more professional jobs for qualified people to fill, rather than simply shuffle the existing labour market pack.

To deny the power of social mobility as an idea suggests that there will always be a working class and that its members should continue to know their place. Simply working to make conditions within the working class better, rather than striving for the transformation of society as a whole so that individuals are not bound by the circumstances of their birth, suggests that people are essentially happy with the status quo.

Why is it assumed that there is a static, immutable pool of people with equally static and immutable working lives? Does a street sweeper need to be a street sweeper his entire life for us to be able to say, "He is a street sweeper and I respect him for that"? Can we not respect him – not to mention pay him decently – for his work whether he undertakes it for six months or 60 years?

Thirty years ago, after mass redundancies in the heavy industries, thousands of laid-off manual workers returned to education, many studying politics and sociology in an attempt to understand how the collective power they had marshalled as union members in the 1970s could have dissipated so swiftly. A significant number became teachers and social workers, while others became self-employed, making a living that didn't necessarily pay better but offered more autonomy.

It's important to make a distinction between economic and social mobility, even though the former makes the latter easier to achieve. In a more open society every individual would have the chance to accumulate educational and occupational experience – if not always money – so that society was not deprived, as it is at present, of so much unused talent.

Some will always regard the very idea of "getting on", or getting away, as an insult to their origins, as even a new form of deference. As with anything to do with class, the politics of social mobility are a tricky and sensitive business. So rather than presenting it as a cost-free golden ticket, as the centre and right are wont to do, or dismissing it as a pernicious myth, as many do on the left, a more useful strategy might be to acknowledge that it has good and bad points, with the burden on individuals being greater the more unequal we are as a society.