This is despite the popular belief that primary schools are largely to blame for Britain's long "tail" of underachievement.
While there has been a sharp improvement in primary school results, many secondaries have still not got to grips with the old problem of educational disruption at age 11, said the School Curriculum and Assessment Authority this week.
A worrying proportion of 14-year-olds is failing to hit the academic targets judged appropriate and the 11-14 age range (key stage 3) is set to be the next focus of official attention. Only 57 per cent of 14-year-olds reached level 5, when the aim is for an 80 per cent pass rate. And only 27 per cent got to level 6, when the Government is hoping for 50 per cent.
SCAA also has concerns about primary schools' failure to go beyond the basics. Spelling is held back by an over-emphasis on phonics, and in maths children are still troubled by division, multiplication and numbers greater than 100.
Overall, the results were described as a welcome improvement by both the Department for Education and Employment and SCAA. Ministers pointed to a sharp improvement in the 11-year-old results for English and maths as evidence that tests are raising standards.
Education minister Cheryl Gillan said: "They provide a comprehensive source of information about how our schools are doing. They confirm that our 11-year-olds are doing better as teachers build on the first year of tests."
She said that more than four-fifths of seven-year-olds exceeded the expected performance and between half and two-thirds of 11-year-olds. At this age there was a rise of 10 percentage points in scores for English and maths.
While pleased with the primary schools' performance, SCAA remains concerned about a failure to go beyond the basics. Junior school spelling is dominated by phonics, and pupils flounder with words like "picture".
Basic number work is good, but pupils have problems with numbers bigger than 100. Boys are disadvantaged by the lack of opportunity to do non-fiction writing - which they prefer. Eleven-year-olds also have problems using calculators appropriately: they are only used for the simplest sums. Older pupils also have problems converting imperial measures to metric.
In particular, however, SCAA remains concerned about results from the early years of secondary school, which have until now attracted less attention than primary school performance.
This week, the Third International Maths and Science Study suggests that British 13-year-olds lag behind many comparable nations in mathematics, although their performance in science is comparatively good.
"In terms of the average levels achieved, we do have a rather wider spread of performance than we would want," said David Hawker, assistant chief executive. "I think there are too many level 3s and 4s at key stage 3 who really ought to be achieving level 5.
"One of the causes of that under-achievement, in my view, is that there's not yet any terribly good curriculum continuity between key stages 2 and 3. I think pupils do go backwards when they get to key stage 3. I don't think schools have got to grips with it yet."
Continuity, he said, is partly hindered by open enrolment, which sees pupils arriving from a wide selection of junior schools. But he insisted that the problem must be solved quickly.
"We have to focus on achievement in Year 9 [14-year-olds]. There's no reason at all to take pupils back to level 3 when they are actually achieving levels 4 or 5 when they come in."
He was supported this week by Professor Michael Barber from London University's Institute of Education. "There are an awful lot of pupils who aren't being challenged," he said. "There needs to be a new focus on pedagogy at key stage 3, getting teaching and expectations sharper."
Six years of SATs, TES2 page11
an eye for spelling ,Tes2 page 14
research focus on the maths and science study, pages 12-13
leader, page 18