Labour leader Jeremy Corbyn says he wants to extend free school meals to all primary school pupils in England.
Mr Corbyn is proposing to cover the cost by introducing VAT on private school fees.
Labour says this would improve the health of many young children at the expense of “ending a subsidy to the privileged few”.
But the Independent Schools Council said the “sums do not add up” for the proposed charge on private schools.
All state school educated pupils in the first three years of primary school already receive free meals, under a scheme introduced by the coalition government.
But Mr Corbyn and shadow education secretary Angela Rayner, visiting a children’s holiday club in Lancashire on Thursday, are going to propose extending it to all primary pupils.
Labour says House of Commons Library figures suggest this would cost £700m to £900m.
Mr Corbyn will say that the price should be paid by parents who send their children to private school – and Labour quotes an estimate from the Fabian Society that VAT on private school fees could raise about £1.5bn per year.
“No child in the UK should go hungry at school. By charging VAT on private schools fees, Labour will make sure all primary school children, no matter what their background, get a healthy meal at school,” the Labour leader will say.
Labour says that there is research evidence showing that universal access to free school meals would raise achievement.
This includes a 2012 report from the Institute for Fiscal Studies – which said that it would raise standards in disadvantaged areas and estimated that it would cost £1bn.
Ms Rayner said that giving every pupil a school meal would remove the stigma of only giving free meals to poorer children.
“While the Conservatives offer tax giveaways to their billionaire friends, they are cutting the schools budget and threatening the health and futures of all our children by denying children the basic right of a healthy lunch at school,” she will say.
The 2014 introduction of free school meals for the first three years was a policy championed by former Liberal Democrat deputy prime minister Nick Clegg.
It remains Lib Dem policy to also want free meals for all primary pupils, putting the cost at £610m a year. But they have not supported the proposal to fund this through VAT on private school fees.
Julie Robinson, head of the Independent Schools Council, said the funding proposals did not add up and would hurt hard working families.
“A third of pupils at our schools are on reduced fees and are from families where both parents work hard to pay the fees,” she said.
“If this measure was introduced smaller independent schools may close, driving more children back to be funded in the state system.”