The Conservative-led education authority is one of only four in England which does not plan to pass on the full increase in education funding from the Government to schools next year.
The heads have warned that they face sending pupils home early or cutting staff unless extra money is found. This week Mr Clarke said he was disappointed by Cambridgeshire and the other authorities: Bath and North Somerset, South Tyneside and Halton.
But he said he would only use his powers to force through arrangements in Cambridgeshire, which had planned to pass on just 71 per cent of the extra funding.
The council has been given a fortnight to respond and plans to consult the public on whether it should appeal.
Keith Walters, council leader, said Mr Clarke's move was "deeply regrettable" and would add a further 3 per cent to council tax bills. The county's heads took a different view.
Jackie Kearns, head of Impington Village college, said her teachers had been highly anxious about next year's funding. "My first reaction was 'Thank God for Charles Clarke'," she said. "We've already made enormous budget cuts and we were looking at increasing our class sizes to more than 32."
Clive Bush, principal of Linton Village college and chair of the Cambridgeshire secondary heads group, said that the council seemed hell-bent on "preserving the sacred cow of having the third lowest council tax in England", no matter what the cost for schools.
Mr Clarke threatened to use the same powers last year against the London boroughs of Croydon and Westminster. But compromises were reached between the councils and the Department for Education and Skills before an order was made in Parliament.
Halton and South Tyneside have escaped intervention because they have agreed to pass on all the money in 20056.
Bath and North Somerset's plans have also been approved because it intends to put extra resources into school building and capital projects and has been supported by its schools forum.