The deal, signed between Government, the employers and all main school staff unions except the National Union of Teachers last January, sets a limit of 38 hours a year from September.

But the National Association of Schoolmasters Union of Women Teachers is arguing that a “no detriment” clause means that individual teachers currently operating below the 38-hour cover limit, at say 10 hours, could not be expected to go any higher from September.

David Hart, National Association of Head Teachers general secretary, claimed the NASUWT’s stance was unacceptable and could be “extremely damaging” to the management of schools.

He said the no detriment clause should only apply to the overall cover systems operated by schools. If it also applied to individual teachers then costs would go “through the roof”.

Graham Lane, Local Government Association education chair, raised the issue nationally, after a local dispute over the interpretation of “no detriment” with the NASUWT in his own authority of Newham, east London.

“It is a great victory that cover has been reduced to 38 hours a year,” he said. “But if you start over egging the pudding with no detriment we won’t be able to run schools properly and will end up sending kids home early.”

Chris Keates, NASUWT acting general secretary, said: “The no detriment clause means that you shouldn’t be doing more cover than you did in previous years, that is absolutely right and there is no variation on that.”

However, she said that schools were supposed to distribute cover evenly among teachers, so individuals should not be on lower cover limits than their colleagues anyway.

The row follows the war of words between the signatories to the workforce deal last week, following the NAHT’s threat to pull out over funding.