Plans to turn all schools into academies could lead to a "poorer education system", a group of councils has said.
Members of the County Councils Network told the BBC the plan set out in a government White Paper could see small schools left without the support they need.
The network represents 37 county and unitary councils, many of which are Conservative-led.
Chairman of the network Cllr Paul Carter, who is also the Conservative leader of Kent County Council and a governor of a multi-academy trust said he thought the plans were being pursued with "undue haste".
He told the BBC: "My concern is that the change will lead to a poorer education system operating across Kent, and more broadly England, because the value that local authorities generally provide to schools will be removed."
He added: "If you have a school with five teachers, and two or three of those teachers become pregnant at the same time, you need those support networks to support those schools - otherwise their finances will not be sustainable and the school will end up in a spiral of decline."
Last month another group of Tory councillors, including the politician responsible for education in David Cameron's own constituency, said the move was wrong for small rural primary schools.
This further round of criticism comes as Education Secretary Nicky Morgan pledged to ensure that rural schools will get the funding they need when a new formula is introduced.
Speaking to The Sunday Telegraph, she said: "I want every school to get the funding it deserves and to ensure that we help rural schools keep their character, independence, values and everything that makes them unique."
She said they had been underfunded for years and the Government was planning to address the unique issues these smaller schools faced.