More than 22,000 additional school places have been created after the education secretary approved 35 new free school applications.
The announcement coincided with the publication of a survey revealing the positive impact headteachers at these institutions believe they are having in raising standards of education in nearby schools.
Some 84 per cent of free schools are working with neighbouring schools, or plan to do so, the survey reveals.
In addition, 72 per cent of headteachers say they are having a positive impact on institutions in their local area - often by competition or collaboration.
Two-thirds of these institutions offer an alternative to the national curriculum in some or all subjects, while around half have an extended school day.
Free schools are state-funded institutions that are independent of local authority control, giving them the freedom to innovate and respond directly to the needs of parents and the local community.
They are mainly located in areas with a shortage of places and a need for high-quality ones - more than a third of the schools recently approved by the education secretary will be in the 30 per cent most deprived communities in England.
At present, there are 251 open free schools and a further 112 are in the pipeline. Once they are fully established, they will provide around 200,000 extra places for pupils across the country.
Education secretary Nicky Morgan said: "Thanks to our plan for education more children in England have the opportunity to go to a good or outstanding school than ever before and free schools have been crucial to that change - with more than two-thirds of free schools meeting this high standard."
Many of these institutions use different admissions procedures to others in their neighbourhoods. One-fifth of those surveyed reported that they were giving priority to pupils from disadvantaged backgrounds.
Four in ten headteachers said term dates at their institutions differ from those in the surrounding area, with some reducing the length of the summer holiday and introducing Saturday learning to increase teaching time.
Posted by Tim Colman