Plans to turn all schools into academies could lead to a "poorer education system", a group of 37 local councils has said.
Conservative-led local authorities are among those warning that the proposals may leave some schools without enough support.
The government has said that it wants to push through the change - which would remove schools from the control of local authorities - by 2022.
Cllr Paul Carter, of the County Councils Network (CCN), warned that the draft plans were being pursued with "undue haste" in an interview with the BBC.
He raised concerns that some schools could enter a "spiral of decline" in times of stress without the support of a wider system.
A Department for Education spokesman said the CCN's concerns were "misplaced" in a statement to the BBC.
The group's warning comes a month after a 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.
Meanwhile, Education Secretary Nicky Morgan has 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 they had been underfunded for years and the Government was planning to address the unique issues these smaller schools faced.