He favours a huge expansion of the assisted places scheme - helping poorer families with school fees - as a way of bridging the gap with the state sector.
Public schools refusing to co-operate should have their charitable status withdrawn, he believes. At the same time, comprehensive schools should encourage the affluent middle classes by reintroducing academic streaming and setting.
Mr Hutton, economics editor of the Guardian, identified the private education system as a major factor both in Britain's economic malaise and in its failure to devote more resources to state schooling.
"I think private education has bedevilled the entire British education debate," he told the Fabian Society. "I think the fact of private education is central to the practice, economics and culture of our education system. " There is, he said, no sense of collective identity or purpose in economic or educational life. British commerce, he said, is still dominated by privately-educated figures who view important decisions as a matter of narrow, shareholder interest.
He believes that the affluent middle classes operate without notions of collective effort, hence Britain is a long way from developing the sort of "stake-holder" capitalism to be seen in Europe - in which decisions reflect a wider range of needs.
He said it was particularly worrying when excellent comprehensive schools in affluent areas such as north Oxford were ignored in favour of the private sector.
One consequence, he suggested, is the comparatively small amount of money spent on educating state pupils. He pointed to the large difference between average day-school fees of Pounds 5,000 a year and the Pounds 2,500 per child spent on a grant-maintained grammar - one of the best-resourced state schools. A pre-prep in wealthy Highgate, north London charges Pounds 7,000 per child, yet a nearby primary school receives only Pounds 1,200 a head.
"As long as the entire middle class are not sending their children to state schools - and that's the situation in the Home Counties - you can't form a coalition that's going to put resources into state education.
"If half the current Cabinet put their children through grammar schools or comprehensives that had streaming, we'd never get an EDX (the Cabinet spending committee which gave education such a low budget) like last autumn's.
"The charitable status of private schools should be made dependent upon at least half their intake coming from the non fee-paying sector of society. The assisted places scheme should be massively expanded and democratised.
"Return Eton to the school that it was originally intended to be."
He also believes that the middle classes would view state education more favourably if there were a return to a policy of academic selection within schools.
"I do think the crucial task is to renegotiate the middle classes into the British education system."
Nor should money be seen as a restriction. Britain, he said, could comfortably afford to pay for a better education system by raising marginal rates of tax: "A 60 per cent higher rate would not be out of line with Western Europe.
"There are large resources available to support education and justifiably so because the social rates of return are astonishingly high.
"For every pound you spend, the social returns are between 12 and 30 per cent. You can more than justify raising the marginal income tax and spending the money on education."