The Independent Schools Council (ISC), which represents 1,200 private schools, says it can provide the 10,000 places if the government pays £5,550 for each pupils – the figure the state system allocates for each child.

The scheme would test some pupils for academic ability, however it will not just target the brightest children. It’s expected to cost up to £80m.

The plan is designed to meet government demands which threaten to strip the tax-free charitable status from private schools that fail to help run or assist state schools.

Under the proposals, independent schools would also collaborate to co-sponsor new state-funded schools in one or more of the six educational “cold spots” in England identified by the Department for Education (DfE).

A DfE spokesperson said: “We welcome contributions to the consultation and will respond in due course.”

Chief Inspector of Schools, Sir Michael Wilshaw, said the plan was not going far enough.

He said: “I think they can do better than that and if I was government I would be asking them to do more as a quid pro quo for their tax privileges.”

Daily fees at independent schools in England currently average around £13,000 a year.

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