An aim of the bill is to give local parents and community groups more say in the running of schools, but the LGIU fears the opposite will happen.
It says that governing bodies coming in to run schools will be "technocrats and people without local knowledge".
The think tank is calling for an assurance that the governing bodies of all schools, including academies and free schools, have local community governors among their ranks.
LGIU policy analyst Frances Migniuolo said: "Community governors are passionate about improving public services, they contribute vital skills and knowledge at no cost to the taxpayer and they care about the needs of local communities and not bureaucratic government targets. They are the army of people that David Cameron asked for.
"The challenge for the coalition government is to roll out the community governance model to other public services, not roll it back where it's working."
The role of governors under the coalition government's vision for education will be discussed at a LGIU conference taking place on 17 June in London called "Stakeholder School Governance Under Threat: What's Worth Fighting For?".
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