Labour has called tax breaks for private schools "inexcusable," as it renewed its call to strip them of their charitable status.
Shadow education secretary Bridget Phillipson said the move would raise vital funds for the state sector.
Keeping the reliefs in place would mean opportunities remained restricted to a "privileged few", she added.
But Education Secretary Gillian Keegan said the "policy of envy" could cost taxpayers in the long run.
Labour's plan could prompt many fee-paying schools to scale back the number of bursaries and scholarships they offer, she added.
Most private schools have charitable status, which means in England and Wales they qualify for at least 80% relief on business rates. This discount was removed in Scotland in April.
Under UK tax law, independent schools are also exempt from VAT on school fees.
Labour argues that ending the reliefs could raise £1.7bn, which it has proposed spending on new teachers, mental health councillors and careers advice in the state sector.
It first announced the plan at its party conference last autumn, but has sought to give greater prominence to the policy in recent months.
Prime Minister Rishi Sunak has rejected the idea – arguing ending the policy is an attack on the "hard-working aspiration of millions of people".
In November, he accused Sir Keir Starmer of making personal attacks on his background after the Labour leader highlighted the effect of the tax reliefs on Winchester College, his old fee-paying school.
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Sir Keir and Mr Sunak sparred over private school status in November
But in a Commons debate on Wednesday about whether to set up a special committee to investigate the issue, Ms Phillipson said that "protecting private schools isn't about aspiration for all of our children".
"It's about ensuring exclusive opportunities remain in the hands of a privileged few," she added.
However, the plan was dismissed by several Conservative MPs speaking during the debate, who questioned whether it would raise the money Labour claimed.
Ms Keegan said the £1.7bn figure "could be over-optimistic" – and schools were already scheduled to receive a cash boost in the coming years.
Many independent schools, she added, might "possibly choose to reduce the bursaries and the scholarships that broaden access to these places" with the resulting drop in discounted places pushing more pupils into the state system.
Quoting research commissioned by the Independent Schools Council, a lobby group, she added that the "ill thought-through" idea "could end up losing money" in the long run.
Conservative MP Simon Hoare also questioned the amount of money that would be raised, calling Labour's plans "a goose which is going to lay the largest golden egg in educational history".
The argument that ending the tax reliefs could lose schools pupils was dismissed by Ms Philipson, who said rising fees in recent in recent years had "far outstripped" wage rises.
The party's bid for a special committee on the issue was eventually rejected, with MPs voting by 303 to 197 to dismiss a motion to set up the group.
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Private school tax breaks inexcusable, says Labour – BBC
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