David Blunkett, Secretary of State for Education, who announced the unprecedented step yesterday, made clear that if a council's services were all failed by inspectors, all might be contracted out.
Individual contracts to run the Government's numeracy and literacy strategies, council budgets and to help failing schools could be worth millions of pounds.
Firms such as the Nord Anglia education consultants, the American-based Edison Project and the non-profit-making Cfbt education services have already put in bids to run a failing Surrey school and are expected to respond to national newspaper advertisements for a list of government- approved contractors.
So far no local education authority has been threatened with new government powers of intervention but ministers are known to be concerned about Hackney, in east London, failed by inspectors more than a year ago.
In a speech which referred repeatedly to the New Labour agenda of "modernisation and reform", Mr Blunkett told the North of England Education Conference in Sunderland: "Where there is consistent failure to deliver adequate services we will intervene. If local education authorities [LEAs] have been doing it badly and doing it badly for a long time, we will transform the service in the interests of children and parents, who deserve better."
Mr Blunkett, whose children went to an inner-city Sheffield comprehensive, said people in poor local education authorities could not afford to buy their way out through private education or by moving house. "Mostly it is in the disadvantaged areas that pupils have had a lousy deal for far too long."
His announcement angered teachers. Peter Smith, general secretary of the Association of Teachers and Lecturers, said: "The Conservatives would never have dared to privatise education by bringing in firms operating for profit.
"Serious under-performance demands serious action but it is not acceptable for private companies to profit from a child's state education."
Councils whose services are found to be failing will have to produce an action plan and accept a private contractor chosen by the Government. Voluntary organisations and neighbouring LEAs will also be able to bid for contracts.
Mr Blunkett dismissed as "very silly" suggestions by council leaders that companies such as Virgin Trains would be invited to improve schools.
And he denied there was a rift between himself and the Prime Minister over local authorities. "He and I are absolutely committed to go on with this transformation."