Changing all schools to academies will cost council taxpayers £320 million, the Local Government Association (LGA) has warned.
The move would also see local authorities lose around £80 million a year in income from business rates, according to the LGA.
The LGA, which represents councils across England, also said converting every school into an academy would have a negative impact on educational standards, as it insisted the government spell out its plans in detail.
Chair of the LGA's children and young people board, Councillor Richard Watts, said forcing schools to become academies would be bad for pupils and educational standards.
"The money that councils are predicted to lose could be better spent on recruiting, training and keeping excellent teachers, and making sure children are safe and have the equipment and support they need, in buildings that are fit for purpose.
"Our recent analysis of the grades achieved by all schools under the more rigorous Ofsted inspection framework proved that 81% of council-maintained schools are rated as 'good' or 'outstanding', compared to 73% of academies, and 79% of free schools.
"These schools should not be forced down the academy route unless they make that decision themselves."
A Department for Education spokeswoman said: "We have the funding to ensure more schools can take advantage of the opportunities presented by becoming an academy, with over #600m available in this Parliament to support schools to convert and build capacity in the system."