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One of the core aims of Jeremy Corbyn’s speech to the Labour conference this Wednesday was to heckle Boris Johnson in his populist, “anti-establishment” pitch to Leave voters, by offering a reminder of the ways in which the prime minister is extremely establishment.

This, and other things at the conference (where the strapline was “People Before Privilege”), reiterated that Labour’s new language of anti-elitism and equality (not social mobility) could have huge ramifications for universities – if the party ever ended up in government. After all, the most selective universities, along with private schools, have an integral role in the construction of social elites.

The Corbyn argument was that Johnson’s attempt to shut down Parliament, derailed by the Supreme Court yesterday, emphasised that he is leading a “born-to-rule government of the entitled” – although you could say that breaking the law is pretty anti-establishment.

Johnson was described as “part of an elite that disdains democracy”, as leading a “government of the privileged few” and a party that is “now claiming to be the voice of the people”, when in reality the Eton and Oxford-educated prime minister “and his wealthy friends are not only on the side of the establishment, they are the establishment”.

The final line of the speech pledged that Labour will “take on the privileged, and put the people in power”. Corbyn briefly mentioned Labour’s pledge to fund HE solely through public funding in this context: “Free education for everyone throughout life as a right not a privilege. No more university tuition fees.”

The political theorist Chantal Mouffe told me earlier this yearthat conversations with Labour figures confirmed to her that the party has been pursuing a left populist strategy. Mouffe advocates left populism – pitching “the people” against “the oligarchy” – as the only antidote to xenophobic right-wing populism. Rather problematically for the left populists around Corbyn, Brexit has interrupted their strategy with its own, very different populist revolt. Corbyn’s speech pretty much shouted: “Hey, Boris Johnson and the Tories can’t be the anti-establishment populists! That’s us!”

The left populist rhetoric has created a climate for some Labour attempts at “anti-elitist” education policy formulation. The motion passed by conference delegates committing Labour to “abolish” private schools included a bid to target the most selective universities (which recruit the most heavily from private schools) by capping their admissions from such institutions.

In practice, it has been suggested that the Labour leadership will continue with the motion’s call to end the charitable status and tax privileges of private schools and ditch the rest of the motion. Nevertheless, under Corbyn, these kinds of ideas are being discussed, and approved, at the Labour conference.

Angela Rayner, the shadow education secretary, reiterated in her conference speech that Labour will “upgrade social mobility to social justice, turning the Social Mobility Commission into the Social Justice Commission”. This move has been billed as focusing on equality for all, rather than social mobility for a few.

Under such an approach, getting more young people from disadvantaged backgrounds into the most selective universities – seen as a route to a fairer society in the social mobility approach – could be dethroned as the dominant narrative in university access. Perhaps inequalities of outcome for graduates of different universities would become a focus.

Under the Conservative government, new Longitudinal Education Outcomes data on graduate earnings have been used as a means of scrutinising perceived “low value HE”: the individual courses at individual universities where graduates earnings are low. The criticism from many in the sector has been that the government is failing to take account of the determining role of students’ social backgrounds, and the variations in regional labour markets, in these earnings figures.

These data indicate, for example, that law graduates from Edge Hill University (an institution based in the Lancashire town of Ormskirk) have median average annual earnings of £19,500 five years after graduation. Meanwhile for their counterparts from the University of Oxford, the figure is £61,500.

Students entering the two universities can expect to encounter dramatically different levels of resources. Edge Hill has a reputation in the sector for being well-run and financially sound, but its net assets total £229 million. At Oxford, university and college assets total £9.1 billion, the Guardian reported last year.

Looked at from a different perspective, the LEO data could tell a story not about institutional underperformance, but about inequality of earnings outcomes for graduates of different kinds of universities and about a hierarchical higher education system magnifying pre-existing inequality.

From this perspective, the most selective universities could be viewed as privilege factories. Those with the highest grades at school, who tend to come from the richest backgrounds, get to go to the wealthiest universities. There, they benefit from the highest levels of teaching hours and the best facilities. After graduation, they gain preferential access to the best jobs and the upper echelons of society, as prestige employers recruit on the basis of university prestige.

If a Labour government were looking to translate a left populist electoral strategy into policy, and looking around for examples of privilege, it might find a few lying around in the university system.

John Morgan is deputy news editor at Times Higher Education.