In the brave new world of elected mayors and cabinet-style local government they would have voting rights over education, civil servants said.
Councils do not have to have an education committee, though most do have. The churches have been particularly worried about losing any say in the running of their schools - if existing committees are abolished.
On some education authorities they hold the balance of power while in areas such as Lancashire half the schools are church schools.
The new constitution checklist produced by the Department for the Environment, Transport and the Regions asks councils to consider the role of parent governors and church representatives and what committees there should be.
Under the draft local government Bill announced last week all councils will have to adopt one of three new arrangements to organise their political leadership:
* a directly-elected mayor with an executive of two or more;
* a cabinet with a leader;
* a directly-elected mayor and council manager.
The draft Bill presumes that all council functions would be carried out by an executive, unless otherwise determined by the Government.
Authorities would, however, be required to set up overview and scrutiny committees. The committee dealing with schools could expect to be consulted on the draft education budget and other major issues before proposals were put to full council.
It would be open to that committee to make its own recommendations to the council.
A spokeswoman for the DETR said: "We envisage church and parent groups being represented with full voting rights as they have now."
The Local Government Association is already reviewing its own committee structure, after concluding it was "too big, too cumbersome and took up too much time for little result".
It is now looking to set up a small national executive body to co-ordinate policy and provide rapid responses, to replace committees with policy forums and create task groups to tackle short-life problems.
The education committee could become the education and lifelong learning policy forum with its own executive for day-to-day business.