In a heated Commons debate last week, Mr Gummer attacked the "untruthful figures" provided by Devon County Council in its appeal to have the spending limit lifted.
The Secretary of State said that Devon was in a position to increase spending on education by 8 per cent, but the council had chosen to give priority to social services, where the budget had increased by 3.6 per cent. And he accused the county of misleading the public and politicians in its presentation of statistics.
Devon chiefs are now seeking a withdrawal of the remarks and considering further action. A council statement said Mr Gummer's comments were "totally unjustified and otherwise defamatory".
The minister has also curbed the spending of Norwich District Council, the three metropolitan councils of Newcastle-upon-Tyne, Sheffield and Barnsley, and the shire counties of Gloucestershire and Shropshire.
Shropshire County Council leader, Sue Davis, said she was "annoyed, bewildered and angry" that Shropshire's budget would stay at Pounds 239 million - Pounds 6m less than is needed to maintain services. About 100 teaching posts are expected to be lost, with adult education and discretionary awards also severely cut.
Only Somerset had its cap increased, by Pounds 2.6m to Pounds 264.9m. Mr Gummer told the Commons that the county council had shown that school budgets would have to be cut unless the capping limit was raised.
Barnsley's spending limit increased by Pounds 2m to Pounds 152.6m, but this was still Pounds 1m less than the council proposed.
Mr Gummer has promised to reconsider the capping system next year following pressure from some of his Conservative colleagues to end it. This year's capping limits on the seven councils are expected to save their taxpayers some Pounds 24m in the current financial year.