Several schools judged as failing by inspectors finished near the top of national league tables for 11-year-olds published this week.
Five of England's top 100 schools for "sustained improvement" in the past four years are failing or seriously struggling, or have been in the past 12 months.
A second table that ranks the top 100 schools for pupils' progress between seven and 11 has four primaries in those categories.
The schools said the results showed the scale of their improvements in recent years.
Stephen Twigg, schools minister, said: "Very often, schools that go into special measures do see rapid improvements, so it would not be entirely a surprise to find schools on both these lists."
His view was backed up by the school which finished top of the list of those making most progress for pupils between seven and 11.
Heath Mount primary, Birmingham, was failing two years ago but is now considered to be doing more than any in the country to help its junior pupils improve.
Another primary finished joint 83rd in this year's most improved list, two-and-a-half years after being failed by inspectors.
Edgar Stammers junior, in Walsall, west Midlands, had seven headteachers in 2002. Its current head, Lee Regan, said: "It was chaos with pupils drilling holes in the blackboard and kicking doors off hinges."
He added that teaching had been transformed, the school had come out of special measures a year ago and it had earned its right to be one of the most improved.
A spokeswoman for the Office for Standards in Education said: "Ofsted is not surprised to see the signs of improvement made by the schools on this list. The majority of schools in special measures show significant improvement over time."
However, Mr Twigg said he would be discussing the good performance of schools recently judged to be failing with Ofsted, amid concerns about how the results can be consistent with the inspection judgements.
A leading academic said the results raised doubts about the tables and the inspection regime.
Professor Peter Tymms of Durham university said the fact that schools could be ranked among the best nationally so soon after damning inspection reports called into question both measures for judging success. He added:
"Something is wrong here, isn't it? Either the league tables are wrong, or the inspection judgements are. Or both."
Professor Tymms, a critic of school league tables, said that in primaries the number of pupils taking tests is small, leaving the schools susceptible to large swings in results each year. It also means that detailed judgements on the quality of a school are hard to make, he said.
The introduction of value-added scores into the tables last year was welcomed by many schools. In particular, many wanted a fairer assessment of primaries' work in improving pupils' performance than that offered by "raw scores" at 11.
But critics have pointed to flaws in the value-added measure. It compares pupils' achievements at 11 with their key stage 2 results four years earlier, but does not take into account factors such as social deprivation.
Ted Melhuish, professor of human development at Birkbeck college, London university, said: "If you do not take into account the characteristics of the pupils and the area, you are failing to take into account some of the most powerful influences on the children's development."
Professor Melhuish is studying pupils' progress at KS2 for the Government using a value-added measure that takes social context into account.
Other critics say the value-added measure makes it virtually impossible for schools in which pupils do well at KS1 to show that they have improved at KS2.
Teachers' leaders said problems with the value-added measure strengthened the call for all league tables to be scrapped.
Mary Bousted, general secretary of the Association of Teachers and Lecturers, said: "League tables have a pernicious effect on teaching and learning."
A top-performing junior school has had its results annulled after investigators said that they had found evidence of widespread cheating.
Waltham Holy Cross junior, in Waltham Abbey, Essex, came in the top 200 schools in 2003. But the Qualifications and Curriculum Authority said that this year, pupils had not completed their work "unaided".
Diane Stygal, the headteacher, denied any wrongdoing.
COUNTDOWN OF THE CHART-TOPPERS
Top five schools at KS 2 (value-added)
1 Heath Mount primary, Birmingham
1 Orrets Meadow, Wirral
3 Vauxhall primary, Lambeth, south London
4 Amberley Ridge, Gloucestershire
5 Clenchwarton community primary, Norfolk
5 Nyland, Swindon
Top five most improved schools at KS 2 (2001-04)
1 Sherington primary, Greenwich, east London
2 Goose Green primary, Southwark, south London
3 Eureka primary, Derbyshire
4 Lowedges primary, Sheffield
5 Old Trafford community, Trafford, Manchester
Top five schools(overall points score)
1 St Michael's Church of England primary, Lancashire
1 Pirton school, Hertfordshire
3 Christ Church, Camden, north London
4 Compton All Saints primary, Hampshire
5 Avonmore primary, Hammersmith and Fulham, London