John McDonnell has thrown his weight behind a campaign to effectively abolish private schools, claiming the institutions "should not exist".
It would involve removing charitable status from private schools, imposing limits on their pupils' entry to universities and for their "endowments and assets to be redistributed" across the wider education sector.
It is unclear yet whether the motion will be selected for debate, or watered down, at Labour's annual conference this weekend in Brighton, but the group said it was "hopeful" it will be adopted by the party.
Support from Mr McDonnell, the shadow chancellor and close ally of Jeremy Corbyn, could also boost the chances of the motion being chosen.
Backing the campaign on Wednesday, Mr McDonnell said: "I hope this campaign will pick up support and eventually become Labour Party policy.
"I think we can gain a large number of votes on the issue, because I believe people think that everyone should have a fair start in life, and that starts by making sure that we all have the same access to education facilities."
He added: "We know that our society is grotesquely unequal, and part of the reason for that is because the inequalities in education particularly in private schools, where large amounts of money are spent on a privileged few."
Responding to the remarks, Labour Against Private Schools campaign group said: "John McDonnell has backed our motion for conference saying he hopes it becomes Labour Party policy.
"This weekend, grassroots members will have a historic opportunity to radically tackle the injustice of private schools."
Rob Poole, a state school teacher from Greater Manchester, who helped organise the campaign, added: "We are delighted that John McDonnell has said he believes private schools should not exist, and that he is supporting our demand to integrate all private schools into the state sector in the next Labour Party election manifesto.
"We are hopeful that our motion will be debated on the conference floor, but we believe it must include our most radical demands.
"Committing the party to removing private schools charitable status alone, for example, won't do enough to challenge the most elite private schools like Eton."
"With Jeremy Corbyn as the most left-wing leader the Labour Party has ever had, this is a historic opportunity to dismantle the private school system which confers unfair privileges and perpetuates inequality."
Labour's last blueprint for government at the 2017 election said the party in power would remove the VAT exemption from independent school fees, and to use the money to introduce free school meals for all children at primary school.
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