Three-quarters of primary heads believe they should be able to devote more time to teaching basic literacy and numeracy.
Many said the primary curriculum is too broad and covers too many topics to be taught properly. As a consequence primary teachers are not spending enough time on "core" subjects and are having to teach subjects they have no expertise in.
"The primary teacher cannot be an expert in 10 curriculum areas," said Maureen Plater, head of St Georges's lower in Leighton Buzzard, Bedfordshire.
Her opinion was supported by a primary head from Surrey: "Children need good basics in numeracy, literacy and logical thinking. The national curriculum for infants is too broad so not enough time can be spent on those aspects which would raise standards."
David Green, head of Old Hill primary, Cradley Heath, Warley, West Midlands: "We need to be able to concentrate on literacy and numeracy and then broaden out into wider subject areas at key stage 2."
This view is shared by David Hart, the National Association of Head Teachers's general secretary. He believes there is a case for a reduction in the breadth of the statutory components of the primary national curriculum.
He said: "Recent pay review research on workload shows the immense pressure teachers are under to deliver the curriculum. Schools need to have some time freed up so they can concentrate on basic skills and I'm sure that will not stop them also providing a broad education."
The union's vice-president Liz Paver believes more time is needed to help children achieve higher levels of literacy and reading skills. She said: "The problem is the massive knowledge base at key stage 2. I think if primary schools can concentrate on getting children to a high level of literacy and teach them to use libraries and advanced reading skills then they will be fully equipped to tackle a wider knowledge base when they move on to secondary school."
But Tony Millns, assistant chief executive of the School Curriculum and Assesment Authority, said there was enough flexibility in the primary curriculum and heads should use their discretion to spend less time on some subjects and more on others.
Only 5 per cent of primary schools band or stream for all subjects, though nearly half (49 per cent) set for some subjects. It is for maths and English that schools most frequently organise their classes into sets and are more likely to do so for key stage 2. A number of schools set for all subjects, but most restrict it for English, maths and science.
This is heartening news for Anthea Millett, chief executive of the Teacher Training Agency, who, in a speech to the Professional Association of Teachers, said primary schools should set or stream their classes and use specialist teachers in order to deliver the curriculum effectively.
She said: "Surely classes, whether in primary or secondary schools, need to be assured of as much homogeneity in their classes as the subject matter needs, if they are to improve pupils' learning."
Ted Wragg, at Exeter University, said that while he thought primary schools have been arranging their classes by ability for some time there has been change within the last year to consider setting.
He said: "There has been a response to public attention. And when schools hear the Labour party talking about it they are having a look at it. Primary schools should be dynamic, and change can be good. Schools are trying out setting and may drop it if they don't think it works."