The Kunskapsskolan approach first emerged as a result of the introduction of a school voucher system in Sweden in 1992. The change allowed independent schools to receive the same funding per pupil from the Government as state schools if parents chose to send their children there.
However, there is one crucial difference with the classic voucher system sometimes called for in Britain - the money cannot be used at schools which charge fees.
None of the private schools in the Swedish scheme are allowed to charge parents. They are independent but completely state funded, which means they can offer families of all incomes a genuine choice as an alternative to municipal schools.
Between 199293 to 200607 the number of voucher funded schools shot up from just over 100 to 900 and today educate 10 per cent of 12 to 15-year-olds in Sweden and 17 per cent of 16 to 18-year-olds.
But left-leaning commentators in Britain suggest the Swedish system, or a version of it, could bring problems such as covert selection.
Paul Holmes, a Liberal Democrat MP, went to Stockholm to see a voucher school from a different chain. Last month he told Parliament: "Although there is a ban on selective admission procedures in Sweden, those wishing to get into the school had to attend seven meetings with their parents - five in the evenings and two lasting throughout two Saturdays - before they could put their names down."
Research by the Swedish National Agency for Education, published in 2003, concluded that its voucher system had increased segregation in Swedish schools - both racially and in terms of pupil performance and parents' education.
The report found that the chance of parents making a choice of an independent or different municipal school increased "dramatically" if they were highly educated.
Polly Toynbee, the left wing commentator, argues that any attempt to emulate the Swedish model will also be socially divisive. The "choice" based system actually restricted choice, she said, because local municipal schools lost bright pupils to independents and became untenable for middle class parents.
Peje Emilsson, co-founder of Kunskapsskolan, said: "It is not like that. The fact that people can choose a school has led to a wider blend and mix of people than when everyone went to the local school."
He points out that in some Kunskapsskolan schools, 60 to 70 per cent of pupils are from immigrant families.
Despite growing interest in countries such as Britain in the Swedish approach, the climate for independent schools in Sweden has cooled in the last two years.
The Government has woken up to the fact that 90 per cent of parents still send their children to municipal schools. Ministers are focusing on raising standards in state schools and allowing them to compete on a level playing field. That means curtailing the freedoms enjoyed by the private sector.
Asked by The TES what advice he would give to British politicians considering following the Swedish voucher system, Bertil Ostberg, state secretary for education, said: "It is important to have the same laws and same rules for all schools, even for independent schools.
"In Sweden, independent schools have a bigger freedom and that is not good. There must be competition on equal terms."
In 2010 his government plans to introduce a new "school law" requiring independent schools to follow the same teacher assessment system and curriculum as municipal schools for the first time.
Sweden's Association of Independent Schools fears the standardised approach will stifle its members' freedom to innovate.
Carl-Gustaf Sta'wstrom, the association's chief executive said. "If you put the same rules and regulations for the independent schools then you have taken away the whole point of having independent schools in the first place, to complement government schools."