In some respects it makes no difference who wins the Conservative leadership contest; whether it’s Boris Johnson or Jeremy Hunt, Britain will get another privately educated prime minister. If – as looks likely – Johnson wins, he will be the 20th Etonian to lead the country, but Hunt went to a boys boarding school too.

But within the Labour party opposition to private schooling seems to be growing at last.

A group of Labour activists is currently circulating a motion to be brought to the party’s conference in September that would essentially commit a Labour government to abolishing private schools.

The motion, proposed by Labour Against Private Schools, comes after history was made last month when for the first time since the 1960s figures within the Labour party joined campaigners from the Socialist Educational Association (SEA) to discuss how to begin phasing out the UK’s private education system. Not since Harold Wilson’s government has Westminster hosted such a discussion regarding the dismantling of Britain’s “educational apartheid.”

Journalists Robert Verkaik and Jess Staufenberg joined Melissa Benn, Steven Longden, Laura Smith MP, and economist Francis Green on a joint discussion panel in the House of Commons on 12 June, chaired by Kate Green MP. Verkaik, author of Posh Boys: How English Public Schools Ruin Britain, and Staufenberg, who reports predominantly on education, both argued that independent schools need to be phased out under Labour, something Green predicted could finally happen under leader Jeremy Corbyn.

Writer and campaigner Melissa Benn, who is the daughter of late Labour MP Tony Benn, advocated for a fairer system in which every child attends the “common school”. Outlawing private schools runs counter to the marketised models of ‘competition’ and ‘choice’ touted by Tory politicians like former education secretary and academy enthusiast, Michael Gove. Instead, campaigners like Benn and the SEA endorse a secular system, based on equality of opportunity, democratic accountability, and collaboration. But while the SEA is affiliated to the Labour party, politicians have previously appeared reticent to support calls for reform.

During the panel discussion, Staufenberg quoted writer Alan Bennett, speaking at Cambridge University in 2017. “Private education is not fair,” she quoted. “Those who provide it know it. Those who pay for it know it. Those who have to sacrifice in order to purchase it know it. And those who receive it know it, or should. And if their education ends without it dawning on them, then that education has been wasted.”

Such ‘unfairness’ is created by linear and chronic social division bred by our parallel schooling system. An independent education is provided for just 7% of the population, but receives three times as much funding per pupil. This tiny 7% attain half of all Oxbridge places, before colonising the vast majority of top jobs. 50% of judges are members of the 7% club, as well as 51% of journalists, 67% UK Oscar winners, 61% of leading medics, and, more topically, 73% (eight) of the original 11 Tory leadership candidates.

Meanwhile, funding cuts to the state sector have left threadbare special education needs (SEN) resources, and further threaten state sector progress. State school teachers (trained at public expense) are regularly poached by the private sector.

During the panel discussion in June, Green stressed how tax breaks for private schools are financed by the public purse. “We are all helping to pay for elite advantage, but only a tiny minority get the benefit,” she said. Green argues that “a more prosperous, fairer, society, needs to tackle the privilege that independent schools enjoy, and integrate them into the state system”.

Verkaik advocates a policy of “slow and painless euthanasia”. But legislation to ban independent schools is unlikely to achieve cross-party parliamentary support, and may not be legally possible. Therefore removing demand for the independent sector by compensating for the advantages they provide, seems to be the most viable route. This could involve restricted admissions to Whitehall and other top public sector jobs and contextual admissions to top universities, a process which aims to make the greatly unlevel playing field between students in the private and public sector more fair by reducing conditional offers based on A-level grades in light of factors such as time spent in care and home postcode. It is currently being trialled at Warwick University.

According to Benn the use of “outmoded and problematic language” to describe our two systems is a major part of the problem. Public schools are known as state schools, with the accompanying connotations of the Stalinist state system. Verkaik explains that the private schools’ ‘public’ label dates back 600 years to when “public school charities actually did charitable things, serving to educate the community’s poor scholars”. As per tradition, they were hijacked by the elite. The SEA advocates a transformation of our hierarchical model, made up of private, selective and “local” schools. Green favours central control of a proportion of private school admissions – up to a third of pupils coming from the local area, gradually rising to 50-75%.

The independent sector plays down Verkaik’s ‘educational apartheid’ in perpetuating the domination of the elite. French cultural theorist Pierre Bourdieu and sociologist Diane Reay view an umbilical link between the social reproduction of cultural and economic capital and educational success. This means that even without private education, inequality will be present and reproduced through wealth. Classrooms in an integrated system will still reproduce social class advantages. But Verkaik views class domination as not being an argument that sidelines the need to end private education. Private schools remain symbolic of government sanctioned social division. This sets the tone for similar behaviour in other social institutions: private healthcare, the fiscal system, housing. Wealth is perpetuating social inequality in modern Britain, currently double what it was in the 1970s.

The example of Alberta in Canada, the highest ranking education system in the English speaking world, suggests that everything that encompasses the construction of a successful public education system could be replicated in Britain, given the political will. It scores highest in minimising the effect on educational outcomes of a student’s economic background; in Alberta the gap between better and less well off is lower than anywhere in any other OECD PISA country. Whilst the province has equitable funding for all students based on a common framework, the system compensates for lack of resources at home, through targeted funding. In Alberta and Finland, private schools remain virtually non-existent.

Despite having models to replicate, no British government has dared tackle private education. It might have been feasible at the time of the Butler reforms in 1944. Following the herculean war efforts of British working class men, and in a wave of post-war welfare state benevolence, Rab Butler aimed to provide universal education to 15. This involved giving local government much greater responsibility for education and inaugurating the tripartite divide. The 1964 Harold Wilson government almost brought an end to the vicious self interest of the independent sector. In 1997 Labour’s huge majority could have at least allowed a start with the abolishing of the assisted places scheme. But the dizzying new Labour Blairite euphoria was led by a man (himself privately educated) unwilling to upset the private school system.

Such a campaign was officially launched on Tuesday. The ‘Abolish Eton’ Twitter handle and hashtag is backed by a number of Labour MPs, including the former party leader Ed Miliband. It seems after nine years of Tory austerity, it is these once unachievable aspirations that are rising again into the political mainstream. It wouldn’t be pie in the sky to think that now would be an appropriate time to begin phasing out of private schools forever.