But more than half of them do see a reduction in the size of infant classes as a key spending priority, according to an interim report by the National Foundation for Educational Research.
In a survey of nearly 1,000 primary schools, 51 per cent of heads considered it more important than spending on textbooks and teaching aids, equipment, school buildings, administrative staff or consumable resources.
The survey shows how pressing is the need to cut class sizes. Since 1994, classes have fallen in fewer than 10 per cent of primary schools and risen in around 40 per cent. The most commonly cited reasons are rising rolls, a school's growing popularity and financial constraints.
Many schools had a class-size policy, with some imposing limits. But 14 per cent of heads said they were unable to follow a policy because they could not effectively resist appeal procedures.
The School Standards and Framework Bill, now going through Parliament, gives the Education Secretary power to set a maximum size for infant classes. Labour had pledged to cut all infant classes to a maximum of 30.
But many heads are worried that statutory limits could reduce school budgets if funding continues to be directly linked to pupil numbers. This would leave them unable to maintain current levels of classroom assistance. They were concerned that there would be more mixed-age or bigger classes at key stage 2. They also wondered how to accommodate extra classes in already crowded schools.
Copies of The impact of class size - an interim research summary can be obtained from the NFER's communications unit on 01754 574123.