They say authoritarian primary heads who oppose the deal are refusing to relieve teachers of more than 20 administrative chores.

The National Association of Schoolmasters Union of Women Teachers and the Association of Teachers and Lecturers cite evidence that some schools have not even begun to implement the deal.

Their threat comes only a month after delegates at the National Association of Head Teachers’ conference defied their leadership and presented ministers with an ultimatum: fund the agreement directly and adequately or we pull out.

Under the deal, tasks such as photocopying and putting up classroom displays should have been transferred to support staff since September.

Chris Keates, NASUWT acting general secretary, said: “There are some schools that have still not started on the contractual changes.”

Mary Bousted, ATL general secretary, said: “Heads will say they are implementing the deal but that is not the message we are getting from all of our members.”

She said a “finger in the wind survey” of ATL officials based in 87 schools around the country at Easter had produced worrying results.

Only seven had fully transferred the administrative tasks teachers were no longer supposed to do, and 43 had made some progress. But 37 schools, or 42 per cent, had done nothing at all.

“Some heads are dragging their heels on this,” she said. “There are some primary heads who rule their schools as mini-worlds, and who do not agree with the agreement. They should get their heads around the fact that these are contractual changes and have to be brought in and things would be a lot easier.”

She expected the spot checks would be concentrated on schools in local authorities identified as causing concern by the government agency supervising the reforms.

Union officials or local authority advisers could visit schools to gain reliable information on what was actually being done. But headteachers said they would resist the checks.

Martin Ward, Secondary Heads Association deputy general secretary, said teachers who believed they were not receiving their rights should raise the matter with their unions.

A TES survey in January found that 45 per cent of teachers had yet to benefit from the deal. In the same month, government figures showed that more than one in 10 schools had not planned how they would make the agreement’s contractual changes.

The disagreement between the unions follows last month’s outspoken attacks from Ms Keates and Dr Bousted on the National Association of Head Teachers after the union’s threat to withdraw from the deal over funding.

At the NAHT’s annual conference delegates presented ministers with their ultimatum over funding the agreement. David Hart, general secretary, said the union would decide whether to stay in the deal in the new year after assessing the three-year funding deal expected in July alongside the autumn announcements.

Rona Tutt, NAHT president, said that the threat by the classroom unions to send officials into schools to conduct spot checks on the deal’s progress would not be in the spirit of partnership.

“There are supposed to be fewer people coming round schools, not more.

There is no evidence that heads don’t want to implement this agreement,” she said.

The Department for Education and Skills said the National Remodelling Team and councils were working with schools to take the agreement forward.

A DfES spokesman said: “It is only natural, and indeed good practice, that local checks are in place so as to ensure that schools are delivering the necessary changes.”