Plans to turn every state school in England into an academy have come under fire from Tory councillors - including the politician responsible for education in David Cameron's own constituency.
Under the Government's plans all schools will have to become academies or be in the process of converting by 2020, taking them out of local authority control.
But Melinda Tilley, the cabinet member for education at Oxfordshire County Council - which includes the Prime Minister's Witney seat - warned small village schools could be at risk if academy chains decided they were no longer viable.
She told BBC Radio 4's Today programme: "It means a lot of little primary schools will be forced to go into multi-academy trusts and I just feel it's the wrong time, in the wrong place, for little primary schools to be forced into doing this.
"I'm afraid there could be a few little village schools that get lost in all of this."
Asked if she was "disappointed" by the Government, she said that was "probably putting it very mildly".
"I'm fed up with diktats from above saying you will do this and you won't do that. This is not why I became a Conservative."
Her concerns were echoed by other senior Conservatives in local government who face losing control of schools in their local areas.
Roger Gough, Conservative councillor in charge of education in Kent, said the policy would cost his local authority several million pounds.
"I don't think there is demonstrable evidence that there is a systemic improvement in performance and certainly not anything that would justify upheaval on this scale," he told the BBC.
Peter Edgar from Hampshire County Council said: "To force all schools would be ridiculously expensive and in my view the wrong thing to do and also could cause in the interim a drop in standards in all our schools."
Arthur Barker, executive member for schools on North Yorkshire county council told the Guardian: "I've no objection to academies. But you need time to do it. You need bodies on the ground. You need dedicated officers to do it.
"One of my concerns is the availability of capacity. It's a big ask. It's a lot of schools nationally."
Ivan Ould, a former head teacher and Tory cabinet member for children and families on Leicestershire county council, told the newspaper: "The Government seems to be determined to take responsibility for anything to do with education away from local authorities.
"If you've got effective local authorities you should take the best practice and expand it across the county. I do not believe a system driven by dogma will meet the needs of children. "