A paper written by John Dunford, general secretary of the Secondary Heads Association, argues that the expertise needed to transform schools already exists in the public sector.
Mr Dunford says that some of the country's best leaders of local education authorities and schools are being lost to the state sector as firms use attractive salaries to lure away the talent they need for school improvement work.
Mr Dunford's paper says: "It is an irony that the Government appears to be wedded to private-sector solutions when the expertise for which the private sector is being given credit comes from... the public sector."
It goes on to argue that the involvement of private companies in running LEAs has been "over-hyped and expensive" while the success rates of such involvement "has not been good".
Mr Dunford points to examples of less dramatic interventions in authorities such as Liverpool, where a chief education officer from another authority and a recently retired CEO were drafted in for a limited period to sort out the LEA's support systems and management structures.
To boost individual school improvement the Secondary Heads Association recommends the establishment of partnerships that include about 10 secondary schools.
Eventually, most of the partnerships would include a consultant leader trained by the National College for School Leadership. Schools with major problems would be able to turn to this consultant for advice.