In a consultation document sent to political parties, they argue that returning admissions to local authorities would "not be in the interest of parental choice". The 650-strong Association of Heads of Grant-Maintained Schools also refuses to surrender control of assets.
Both main political parties are reviewing their policy on GM schools. While the Education Secretary Gillian Shephard is looking at ways of increasing the attractions of opting out, Labour is drawing up plans for a new local framework for LEA and GM schools.
The association, however, says: "In planning the future development of education in England and Wales it is essential that the challenge provided by grant-maintained schools . . . should not be diluted but must be strengthened. "
It suggests the planning function shared between the Funding Agency for Schools and local education authorities could be extended to include responsibility for creating and removing school places as well as approving admissions criteria.
Alternatively, it moots regional planning and funding boards or a local council of grant-maintained schools within each LEA which would represent opted-out schools in discussions with the council on admissions and planning.
It criticises the "gross inequities" of school funding across the country, which it claims are "very much a product of local authority decision-making" and urges the Department for Education to move "more rapidly" towards a national funding formula.
It says that the Standard Spending Assessment - the Government estimate of how much should be spent within each authority - could be used as a basis.
But the association says it may be more appropriate to move to regional planning and funding boards, and the development of regional funding formulas.