The Department for Education and Employment named 18 authorities, saying David Blunkett had written to them urging them to reconsider their budgets.
He told them to ensure all the extra cash in the education standard spending assessment was spent on the service.
His letter angered many of the councils which claimed they had passed on the full increase. Some said they were spending more than the Government thought necessary.
Among those authorities to have complained are Dorset, Hertfordshire, Somerset and West Sussex.
Trevor Jones, leader of Dorset, told Mr Blunkett: "You have clearly been misinformed because the county council's spending on education in 1999-2000 will far exceed the Government's yardstick."
John Metcalf, leader of Hertfordshire, said: "We were quick to respond stating the actual position. We have received a further letter acknowledging that Hertfordshire's 1999-2000 education SSA increase will all be spent on education."
John Freeman, deputy director of education at Somerset, said the county had not received a letter.
And Neil Matthewson, West Sussex's education committee chairman, said:
"West Sussex gives the highest priority to education. We are spending pound;12.75 million more than the Government guidelines."
A spokesman for the DFEE said: "Where there were clear indications that an LEA was not planning to spend its extra cash for education purposes, we contacted them to encourage them to do so.
"It is essential that when more money is being provided than before, that money is used for education."