The Government's recently-published local government White Paper encourages councils to try out different management structures.
The London borough of Hammersmith and Fulham is experimenting with an executive mayor and six-strong board of deputy councillors. But concerns have been raised about where parent-governors and church representatives would sit.
Church of England diocesan authorities are taking legal advice over the council's arrangements, which dispense with a traditional education committee. Cabinet decisions are scrutinised by a cross-party council committee and ratified by a six-member panel.
But none of these three bodies has places for non-councillors, despite the new requirement in the School Standards and Framework Act that any committee dealing with education must include at least one parent-governor. Local education representatives have been promised places on review panels.
But the White Paper promises: "There will continue to be Church and parent representatives on any council committees which are concerned with education. "
Local government minister Hilary Armstrong added: "we will make sure parents and church representatives can sit there".