They fear that a dip in their schools' score could lead, in the worst cases, to them losing their jobs. The pressure that primaries are under is indicated by the 53 per cent of them who feel the need to help Year 6, usually by tutoring groups of children themselves.
One headteacher, on The TES website, said: "In my previous school our results dropped below the floor targets and we ended up with local authority advisers crawling all over us. The pressure to 'improve' or at least look like we were was intense."
Chris Davies, spokesman of the National Primary Heads' Association, said: "When Ofsted comes in, the test scores are the first things inspectors look at. A bad report leads to the school being clobbered in the local press, parents withdrawing children and at worst a special team being put in to run the school and the head removed."
The high-stake tests in English, maths and science are taken by 650,000 11 year-olds each May.
This year, the TES survey of 82 schools found that English results may rise again this year after stalling in 2006. Headteachers said that on average their KS2 English results were up 1 percentage point on last year and maths had risen by 5 percentage points. If repeated nationally, this would mean results rising from 79 per cent to 80 per cent in English and from 76 per cent to 81 per cent in maths. Science scores were also predicted to go up 1 percentage point, meaning a rise from 87 per cent to 88 per cent if repeated nationally.
Preparation for tests in lesson time takes an average of nine hours a week in January of Year 6, building up to 12 hours a week in April, The TES revealed earlier this year.
Jesmin Begum, 11, and Nadim Ahmed, 11, of Westwood primary in Oldham, took the tests in May. In the spring term, they did their usual literacy and numeracy lessons in the morning, plus one other subject. Then after lunch they would take an extra class in either English, maths or science and a final lesson in a foundation subject.
Anne Ladbrook, head of East Worlington primary in Devon, takes classes for half a day a week at the 50-pupil school. "Some schools stop their normal timetable and do Sats preparation," she said. "We don't but with English, maths and science we step things up."
The government target is for 85 per cent of pupils to reach level 4 in English and maths by 2008. In September, 10 authorities will start to trial externally set progress tests. Neither Scotland nor Wales publish primary test results.
Tests on trial, pages 16-17
Leading article, page 26