Fears were raised at the Scottish Labour conference in Dundee that measures in the government’s Education Bill will undermine councils.
The bill would see sweeping reforms to the school system, including the introduction of a new Headteachers’ Charter, giving heads more power over the curriculum, recruitment and budgets.
However, the EIS teaching union has already warned only a minority of headteachers and deputies backed the move.
Labour education spokesman Iain Gray told the conference the proposals had been “rejected by parents, by teachers, by educationalists” as well as by some SNP run councils.
Mr Gray said: “John Swinney says it’s about empowering schools, but it is really about disempowering councils and centralising control with the very government who have so badly mismanaged our schools for 11 long years.
“It is just the latest assault on local democracy, the right to take local decisions about local schools. That is not what our schools need.”
Activist Leah Franchetti said she was “extremely disappointed with John Swinney’s reform agenda”.
She told the conference: “His governance review serves one purpose only – it undermines our councils and gives his government control over education and removes local democratic accountability.”
Ms Franchetti added: “You’ve seen the disaster of Police Scotland and the Scottish Police Authority, whose toothless board members are handpicked by the Justice Secretary.
“Imagine what it would be like if John Swinney’s cronies became the beneficiaries of his educational power grab.”
While First Minister Nicola Sturgeon has made closing the attainment gap in schools her top priority, Ms Franchetti said the government would fail to achieve this.
She said: “There is a reason why the SNP government will not close the attainment gap, substantially or otherwise. The SNP is a nationalist party not a social justice movement.
“SNP MSPs do not wake up with a burning sense of injustice about inequality, they rise every morning. They rise every morning with a burning sense of anger about being in a political union with England.
“Their passion is constitutional, not social, economic or educational. Labour says ‘education, education, education’ the SNP say ‘grievance, grievance, grievance’.”