Headteachers are opposed to giving local authorities a greater say in the running of schools, but there is some support from unions representing classroom teachers.
In its response to the Government's White Paper, Excellence in Schools, the National Association of Head Teachers shows its reluctance to give up powers gained through local management. "It is quite inappropriate for authorities to approve school targets, and quite outrageous that they should be given the power to evoke an early warning system where it fails to reach agreement with the school on targets," it said.
The union does not want local councils to be involved in the appointment of headteachers, but does see a role for them in governor training.
In contrast, the Association of Teachers and Lecturers, which does not represent heads, believes an LEA should have a "right and duty to report to a governing body any concerns it may have about a head's performance".
There is agreement, however, that the Government's plans to make councils delegate more money to schools is at odds with the expectation that they will play a greater role in target setting, assessing school performance, co-ordinating admissions and training.
Many councils have run down their inspection and advisory services, especially in areas with many grant-maintained schools.
The National Union of Teachers and the ATL warn that the Government must not over-emphasise the role of the head in raising standards. "A dearth of continuing professional development followed by intensive headteacher-related in-service will not lead to the development of the rounded and appropriately experienced professionals," said the NUT.
"Put bluntly," said the ATL, "there is no shortage of cases in which mediocre managers are effectively carried by teachers committed to children."
Attempts in the White Paper to enhance the careers of ambitious or high-flying teachers is met with little enthusiasm. The fast-track to headship causes concern because, according to the Staffordshire branch of the NAHT, it could mean that "future heads do not get the diversity of experience and responsibility that should be available in the normal course of promotion".
The unions also fear that fast-tracking will be used inappropriately to plug headship vacancies. The new grade of advanced skills teacher is similarly viewed with scepticism, either because it removes good staff from the classroom to act as mentors or threatens to reincarnate advisory teachers.
The unions worry that the Government is treading on the profession's toes. They do not want to have literacy and numeracy hours imposed upon them, nor do they believe it is the Education Secretary's job to decide how much homework children should do, or to push setting.
The Professional Association of Teachers is not alone when it questions the Government's championing of specialist schools: "We think there is an arguable case for all schools, especially secondary ones, to strive to be specialist schools."
The unions add to a growing consensus that foundation schools - expected to be the successor to opted-out schools - will be divisive. The ATL claims the only reason to become a foundation school is for status.
The unions are at pains to show they share the Government's ultimate aim to raise standards. They also welcome the fact that they have been consulted and have responded with thoughtful submissions to the Department for Education and Employment.
"All schools would wish to become part of a 'can do' culture, but support, both in words and deeds, is absolutely essential," said the NAHT.