What business does the private sector have running state schools?

Fifteen years ago, a late-night chat between Professor Michael Barber, the then Labour education guru, and a man called Benno C Schmidt sent a frisson of horror through much of the educational establishment in the UK. Schmidt was then the chief executive of Edison, the largest private-sector operator involved in running state schools in America, and he was keen to find out how the for-profit company could play a similar role here.

It took five years for that first foray into the British education scene to eventuate, with the setting up of a subsidiary company, EdisonLearning, and the shedding of its US links. Even then, there were still reservations about what sort of role the private sector should play in education – and there are those who still have doubts today.

But EdisonLearning persevered. It is now an essentially British operation – its managing director, Tim Nash, and most of its employees are former UK teachers – and it is celebrating its 10th year of partnerships with schools in the UK. Those partnerships numbered 200 at last count.

Since its creation, EdisonLearning has also set up eight academies and is piloting an alternative inspection service with leaders of the National Association of Head Teachers that can give schools an early warning if they need to improve.

One of the first schools to form a partnership with EdisonLearning was Lyons Hall primary school in Braintree, Essex. "We were a little bit edgy," its head teacher, Andrew Smith, says. "It was just after Iraq, and there was a bit of a feeling about getting involved with an American company. They were very into talking about integrity and we were sort of, 'oh, no, it's very American – not British'."

Lyons Hall cautiously signed up, though only for a year so that either party could back out of the deal if it didn't go well. A decade on, they are still working together. "When EdisonLearning came forward with their ideas, there was not one thing that we would disagree with," says Smith.

The school had been struggling with numerous behavioural and attainment issues when Smith took over as head in 2002. Those problems still needed to be tackled when EdisonLearning came on to the scene 12 months later. Now the school is flourishing, the latest report on it by Ofsted, the education standards watchdog, rated it as "outstanding", and this year there were 259 applicants for the 60 available places.

EdisonLearning supplied the school with its core learning values: compassion, wisdom, respect, justice, courage, hope, responsibility and, that word, integrity. The idea then was to instil these values into all staff and pupils. "It's like Cape Canaveral," says Smith. "If you ask a cleaner there what their job is, they'll say it is to help with the US space programme. Ask a cleaner here, and they'll say they're helping children to learn."

The company introduced the school to "FISH! philosophy" – which was inspired by the Pike Place Fish Market in Seattle. Despite their smelly, cold environment and repetitive, tiring work, its employees were encouraged by their managers to enjoy themselves, and, in doing so, became attentive to their customers and very productive.

"It was a question of doing something slightly different," says Smith. "Under the previous headship, they toed the party line, but this allowed us to be slightly different. We wanted to show the pupils you can have fun from learning."

The school has also developed its pupils' confidence by insisting that any visitor to a classroom is greeted with a handshake by two of the pupils who must introduce themselves.

The makeover has led to other schools from around the country visiting Lyons Hall to see how it has turned itself around. It is now a teaching school, which means that would-be teachers can train on the job. "It also means that we can pick the cream of the crop and offer them a job here," says Smith. There are conference training facilities for staff from other schools and a portable classroom in the playground offers one-to-one tuition to struggling pupils on the verge of exclusion from other schools as they prepare to return to the classroom. In the past year, Lyons Hall has had 4,700 visitors trying to learn from its experience.

Willow Brook school, which serves a more disadvantaged area in Colchester, Essex, is one of EdisonLearning's most recent partnerships. It has a chequered history – opening as a Fresh Start school in 2004 with just 90 pupils (Fresh Start was a Labour initiative under which failing schools were closed down and reopened with a new name and a new staff).

The school is still rated by Ofsted as "requires improvement" – the category that has replaced "satisfactory" in the inspectors' lexicon. However, Willow Brook's head teacher, Joanna Newitt, is optimistic that it will reach the Government's minimum target for the percentage of pupils obtaining the expected standard in maths and English Sats for the first time next year. "We would have reached it this summer," Newitt says, "but I insisted on keeping six pupils in school who could have been excluded." In a school where only 20 pupils sat the national curriculum tests for 11-year-olds, that had a major impact on the overall standard.

The curriculum package created for Willow Brook by EdisonLearning is similar to that supplied to Lyons Hall but it was negotiated with the school's leadership to take into account specific local circumstances. "Edison has provided us with a whole raft of things that we have now taken on as our own," Newitt says. What she particularly likes about the company's approach is that it does not operate like some other sponsors and say: "This is what you do – now get on with it." She describes the method of operating as "prodding, not poking".

In the time since Benno C Schmidt first dipped his toe into the water on this side of the pond in 1998, the attitude to private companies' involvement in helping to run schools has changed dramatically. Many of England's 3,000-plus academies are sponsored by academy chains and Edison has been quick to jump on to that bandwagon, too, setting up what it calls the Collaborative Academies Trust as a new "not-for-profit" chain, with schools in Northampton and the Bridgwater area of Somerset.

So far have things progressed that right-wing Conservatives are now anxious to put a commitment in the party's 2015 election manifesto that would allow private companies to make a profit out of running schools. Their argument, that this is essential to getting more companies to come forward, is an argument also put forward in Sweden, which the Education Secretary, Michael Gove, used as a model for his free schools (run on academy lines). Swedish educational advisers believed that the free-schools experiment would fail in the UK if private sponsors were not permitted to make a profit.

Even without introducing the profit motive, though, there are still teachers' leaders who have reservations about private companies' links with schools. "Edison's track record in neither the US, where it has run for-profit charter schools, nor the UK, where it is an expanding academy chain, suggests that it has a magic formula to improve schools," says Christine Blower, the general secretary of the National Union of Teachers.

"Experience in both the US and UK shows that changing the structure of a school and handing it over to an unaccountable private company or academy chain is no guarantee of quality. The Secretary of State is driving forward his academy and free school project in defiance of the evidence and it is clear that his real ideological commitment is ultimately to the introduction of profit-making schools in the UK."

That remains to be seen. What is clear from EdisonLearning, though, is that this is not part of its own agenda in the UK. Nick Ridley, the company's head of sales and marketing, says: "It's not something we're particularly interested in. It is a non-argument as far as we're concerned."