It was commissioned to address primary heads’ concerns about a lack of funding to allow teachers to spend 10 per cent of their timetable on planning and assessment. Some heads have been forced to take extended singing sessions for the entire school to free teachers. Others had been shocked by the cost of hiring sports coaches or other specialist instructors.

A further hidden cost was in backdated pay rises. The TES revealed last month that local authorities, including Staffordshire, were telling schools they would be liable for millions in back pay.

The report was prepared by George Phipson, a funding consultant to the National Association of Head Teachers, with the assistance of Dame Pat Collarbone, the government official who led the school remodelling drive.

The government intention in school workforce remodelling was that schools use support staff, on lower salaries, to perform less-specialised duties. That sparked NUT concerns about cheaper workers doing teachers’ jobs.

The report finds that a pound;170 million top-up for the smooth introduction of the workforce agreement should have been sufficient. But schools’ attempts to use qualified teachers or higher-level teaching assistants proved unaffordable. The report says some money was not passed to schools by local authorities.

The findings are not welcomed by the alliance of unions, employers and the Government whose work led to the introduction of guaranteed preparation time.

The NAHT always insisted primary schools did not have funding to give teachers one hour in every 10 out of the classroom. Unhappy at the Government’s refusal to increase funding, it walked out of the social partnership in 2005.

The Department agreed to fund the study in January as part of an agreement in which the NAHT rejoined the alliance.

Mick Brookes, the association’s general secretary, said the report showed that the original funding levels had been insufficient. “There has been above-inflation funding for schools for the past few years, which has enabled many schools to reach a sustainable situation,” he said. “We’re aware that some schools have still identified problems with sustaining PPA time.”

But Martin Johnson, acting deputy general secretary of the Association of Teachers and Lecturers, said the money was sufficient.

“The real problem is that too few heads have the financial expertise to take a look at their resources and the best way to spend them,” he said. “They have relied on generic local authority models.”

John Freeman, joint president of the Association of Directors of Children’s Services, said an Audit Commission analysis showed no evidence of local authorities holding back money.

“This year’s funding settlement is tight,” he said. “For some schools, like those dealing with falling rolls, it will be difficult to balance the budgets and they may need to make redundancies. But in general, the money is adequate for schools to staff themselves.”