The move comes amid a dispute between the authority and the school over events following the fire, which destroyed a large part of the school.
Shropshire county council has now warned GM schools it will provide only immediate emergency help to the opted-out sector.
Carol Adams, county education officer, said the authority could not "engage extensive staff time in providing advice and help with rebuilding if schools have chosen to go GM".
Versions of events following the fire at Greenacres, an opted-out primary in Shrewsbury, earlier this year vary between the authority and the school.
The council said it commissioned local contractors to board up the damaged building, and some days later called in a demolition contractor.
Its senior building surveyor, who was on duty that weekend, was contacted by Shropshire Fire and Rescue Service, which requested assistance.
The county said it had no formal responsibility to respond the way it did. It also has no responsibility for rebuilding the GM school or for the provision of pupils' education in temporary accommodation.
However, immediate emergency assistance was authorised by the county education officer and chair of education on the basis that the school accepted the full cost of the help.
David Challoner, the headteacher, said the surveyor, called in by the fire officer who did not know the different status of the school, had said his department could take on the emergency work on an independent contract basis. "The LEA said they'd organised it and done it; but they certainly did not, " he said.
The insurance loss adjusters negotiated a contract with the estates department surveyor on the Monday morning. There was no representative from the education authority present, and "I've not spoken to one since the fire about offers of help".
The Funding Agency for Schools (FAS) said it had given Greenacres help and advice, particularly on how to claim insurance. A new school will have to be built. Mr Challoner said the FAS had offered help, but there was no need.
The council said the experience at Greenacres Primary contrasted with that at Phoenix School, an LEA school which suffered a major fire at the end of 1995.
It said there were very significant differences, particularly in relation to the head's role.
"The head at Phoenix feels he has been able to concentrate his efforts and those of his staff on the educational aspects of running the school in the aftermath of the fire.
"He has had the burdens of the fire and the implications for the school accommodation removed from him by LEA officers, and it is they who have concentrated on dealing with the accommodation and site issues and the involvement with the loss adjuster and insurance company."