Rules tightened on extra time
And 3,500 fewer 14-year-olds were allowed more time to complete English, maths and science papers in 2003.
The numbers fell because the Qualifications and Curriculum Authority revised its arrangements last year.
Children with statements of special needs automatically get 25 per cent extra time to complete the tests at a school's discretion.
But for these children to have more than 25 per cent extra time, or for other children to have any extra time, schools must apply to their local authority or the QCA.
The QCA clarified the rules after the number of 11-year-olds allowed to have extra time rose by 25 per cent from 30,000 in 2000 to 38,000 in 2002.
This year, 28,000 or 4 per cent of 11-year-olds in state schools, were given extra time compared to 6 per cent in 2002.
There was a similar drop in the number of 14-year-olds allowed extra time, down from around 13,000 in 2002 to 9,500 in 2003.
Schools can apply for extra time for children who, for example, have special needs, receive additional time on a regular basis, have a recommendation for additional time from a physiotherapist, occupational therapist or qualified specialist member of staff, or if the child's reading age is two years lower than their cognitive ability.
But additional time is inappropriate for children working below the level of the test, who do not regularly receive additional time or if the child's needs are better catered for by rest breaks or working in a separate room.
Jackie Bawden, QCA head of assessment, said: "We tried to simplify our instructions to both teachers and local authorities. We wanted children who needed more time to get it, but did not want to produce extra work for teachers who were completing forms which would not be approved."
The QCA said not every child who is allowed extra time goes on to use it.
Mike Collins, education adviser of the National Autistic Society, said: "It is the responsibility of schools to make sure they read the guidance and have applications in on time. They should be thinking about it in the autumn term.
"I get phone calls very late in the day from anxious parents who say their son or daughter is doing Sats in a week or so and they can't do this or that. But by then it is too late."