Private companies have been making money from state schools for decades. They have sold them books, computers, furniture, advertising space, and, more recently, management services.

But one thing has remained strictly taboo: the idea that a private company should have complete control over a state-funded school and make a profit.

Even the Conservatives, while enthusiastic about the benefits that private providers could bring, have suggested this is a step too far.

But there are signs that change could be on the way. Ed Balls, Children, Schools and Families Secretary, said last month that he will consult on whether private companies should be allowed to run pupil referral units on behalf of local authorities and make a profit.

Few appeared to register the significance of the news. Legally, pupil referral units are state schools, so if it is all right for them, then why should companies not run secondary or primary schools at a profit?

That is certainly the thinking of those on the right who argue it would lead to the diversity in state education that they view as key to raising standards.

Sam Freedman, director of education at Policy Exchange, the right-leaning think tank, said: “It is going to be a long process of political acceptance, but it will come eventually because it is the logical extension of the model.

“If you want to build up alternative providers, you have to encourage them to come into the system.”

Alternative providers already exist, of course, in the form of sponsors of chains of academies such as the United Learning Trust, Oasis and ARK (see panel). In a sense Kunskapsskolan, the Swedish private schools company, is just the latest of these - an organisation prepared to run state-funded schools on a non profit basis.

But it differs on two important counts. First, the Swedes plan to offer the most radically different version of education to date.

Second, the company is not a charity and is quite open in saying it would like to make a profit from British state school operations.

Until that happens, Kunskapsskolan is happy to use them as a way of proving that its model can work in an English schools system, while making money from the low-fee private schools it also plans to open here.

The fear for free marketeers is that other companies might not be prepared to play such a long game.

A halfway house suggested by Policy Exchange would see sponsors who are prepared to run networks of state schools given grants of, say, pound;200,000 per school.

This would be an about-turn for an academies system that has traditionally expected sponsors to contribute something in return for controlling schools.

But Mr Freedman believes it would give them the capacity to develop a genuinely distinctive model for their schools.

In the end, however, it is profit that is likely to tempt other private providers, such as Global Education Management Systems and Edison, into running state schools.

The irony, certainly as far as Kunskapsskolan is concerned, is that those most opposed to the idea of profit are the people most likely to be interested and enthused by the progressive liberal version of education it offers.

As Mr Freedman puts it: “If the left was just prepared to let the market structure come into education, they would get a lot more out in terms of getting the progressive education that they want.”