Heads predicted 18 months ago that results this summer would plateau in English at 79 per cent but would rise to 80 per cent in maths. The Government has said that it wants 85 per cent of Year 6 pupils to reach the expected level 4 in English and maths by next year.

A survey of 82 schools by The TES last month found results had risen on average by 1 percentage point in English and 5 percentage points in maths.

In May, about 650,000 11-year-olds sat papers in reading, writing, maths and science. But Bob Knight, headteacher at Darlinghurst primary in Southend, Essex, where children mirror the national average, said the results show nothing new to primary teachers and, anyway, they are not used by secondary schools. “Teacher assessment is so accurate,” he said, “that we are confident that this would do the job just as well as the Sats process.

“It’s very frustrating as a primary practioner. Children tested at end of key stage 2 go forward with a set of results, then the majority of secondary schools ignore them because they prefer to do their own testing not long after children arrive. How does that suggest to the children the value of tests?

“What it is saying is that we only trust our own tests.”

At Darlinghurst, preparation for the Sats begins in September. The school tries to keep a normal timetable, but a little more English, maths and science is taught. Then exam lessons are introduced so, by the time the tests start, pupils will have done five or six practice papers. “If you talk to the children, they do feel that the fun goes out of school,” said Mr Knight.

Next term schools will be required to introduce synthetic phonics into all reception classes, following a review of reading. Mr Balls has announced a similar review into primary maths.