Academies, the controversial "independent state schools", are proving popular with parents, says an ongoing progress report.
Ministers intend to expand the programme to 400 schools
Each year, PriceWaterhouseCoopers management consultancy evaluates academies for the government.
The latest said the 42 academies, many replacing failing schools, had had to turn away more than 15,000 families who were seeking places.
But the report warned that behaviour was "still a challenge" for academies.
The academy project will create 400 of these independent state schools - which are non-fee charging and non-selective, but which have outside partners, high levels of investment and greater autonomy.
Many were built in areas of deprivation with a legacy of educational underachievement.
Since the academy scheme was launched, PriceWaterhouseCoopers has regularly evaluated their progress.
This latest report shows that only three of the 42 academies are not oversubscribed - with some of the more popular academies having more than 1,200 applications for 180 places.
And the government has highlighted that exam results are improving more rapidly than average. The report says academies "generally exceeded corresponding improvements at a national level and amongst other similar schools".
However the report cautions that these are schools which face "huge challenges" and even though results are rising they are often starting from a "very low base".
But as the schools become more established and gain a reputation, the report also notes how rapidly the social profile of the schools' intakes could change.
There were some academies which saw a sharp fall in the numbers of pupils on free school meals, while others had seen a sharp increase.
But all the schools, apart from one, had a higher proportion of children on free school meals than the national average entitlement - with many having three times above the average of 14% for England as a whole.
Whether academies succeed in the longer term will depend on whether they can overcome some of the deep-rooted problems of their predecessors - such as poor behaviour and truancy.
And both of these issues remain problems. "A small number of academies still have high levels of absences," says the report.
Last week, figures were published showing that academies expelled pupils at twice the rate of other secondary schools.
Both the government and Conservative opposition welcomed the latest evaluation report.
"The best endorsement of academies is their increasing popularity with parents. The latest application figures show an average of three pupils for every academy place this September," said Schools Minister Lord Adonis.
Shadow Schools Minister Nick Gibb said: "This report confirms that the academy programme is producing schools that are popular with parents and which provide an increasingly high quality of education, which is why a Conservative government will continue with the programme and expand it."