It’s early afternoon in Lintulaakson school in Espoo, near Helsinki. The younger children are having a snack before starting their after-school activities. Upstairs a group of 12-year-olds are in a craft class, cutting patterns and making clothes on sewing machines.

Outside, children play in an enormous outdoor space, equipped with a climbing frames, football pitches and basketball courts. “Hey, Petteri,” one boy yells casually at the principal, Petteri Kuusimäki. “Next year can we start school a bit later, at 10am?” Kuusimäki jokes with them. It’s all first names here.

The Finnish education system is the envy of the world. Along with Tove Jansson’s Moomins, Nokia phones and Iittala glassware, it has become one of the country’s most celebrated exports – and it’s easy to see why.

Its students consistently score well at the top end of the Pisa international league tables, and as Kuusimäki walks me round his school he describes a kind of education utopia – a place where teachers are highly trained, revered and trusted, and children’s wellbeing is paramount.

Facebook Twitter Pinterest Pupils in the school cafeteria at lunchtime. Photograph: Miikka Pirinen/The Guardian

There are no Ofsted-style inspections, no streaming by ability, no national exams until 18, no school uniforms, no school league tables and no fee-paying private schools.

At its party conference this week, Labour committed to follow Finland’s lead and not only scrap Ofsted but abolish private schools by forcing their integration with the state sector. Explaining the policy, the Labour leader, Jeremy Corbyn, told BBC Radio 4: “In some countries, it is not allowed to charge for education in any form … in Finland, for example.”

The British Labour party is far from alone in its enthusiasm for the Finnish education system. Every year hundreds of delegations of teachers and policymakers from all over the world pour into Helsinki to see this nirvana for themselves. So popular has it become that international visits are strictly regulated and have to be paid for – a presentation costs €682 (£607) per hour and a school visit €1,240.

Facebook Twitter Pinterest A classroom discussion. In Finnish school’s children’s wellbeing is paramount. Photograph: Miikka Pirinen

In the past two months there have been groups from Israel, Brazil, China and Korea. In the coming weeks there will be visits from New Zealand and Lithuania.

Meanwhile, Finland’s influence is spreading far and wide. Last month a school opened in Ho Chi Minh City in Vietnam based on the Finnish curriculum and pedagogical approach, with Finnish staff on the teaching team.

Kuusimäki tells me Finland’s schools are well-funded and built around the principle of equality of opportunity for all pupils. He is baffled when I try to explain that some state schools in England are so strapped for cash that they are asking parents for donations. “As you may know, everything is free in Finland,” he says, university included.

There is just one fee-paying school in the country, the International School of Helsinki, which has mainly catered for international employees of Nokia and other industries. Otherwise, charging fees is illegal and parents are happy by and large to send their children to their local school. “We really don’t have bad schools,” Kuusimäki says.

Facebook Twitter Pinterest Pupils hang out in the school yard. The school has an array of climbing frames, football pitches and basketball courts. Photograph: Miikka Pirinen

In class children are listened to and respected, school lunches are free, detentions are rare and exclusions pretty much unheard of. Kuusimäki gave his last detention 15 years ago, and is visibly horrified at the idea of excluding a child from school. “As a principal, you can’t think like that. We are responsible for these children and their lives. We can’t give up.”

But things are changing slowly. Schools are becoming more diverse – 20% of pupils at Lintulaakson school are from immigrant backgrounds, elsewhere it is 75%. The curriculum has been revised and Kuusimäki says more has had to be done to stretch gifted children.

Facebook Twitter Pinterest Principal Petteri Kuusimäki gave his last detention 15 years ago. Photograph: Miikka Pirinen

A compulsory pre-school year for six-year-olds has been introduced to help with school-readiness, and there is talk of starting even earlier, while the minimum school leaving age has recently been raised to 18. Meanwhile, parents “shopping for schools” is on the increase.

Finnish education experts would be the first to admit they do not have all the answers and methods in one country do not always translate to another. John Jerrim, professor of education and social statistics at the University College London Institute of Education, does not believe England should be looking to Finland. “Its Pisa scores have actually been in decline. And there is no reason to believe their high scores on international tests are due to their schools. So there is no reason to try to copy Finland.”

Facebook Twitter Pinterest Second-graders Menni Pietiläinen (left) and Nathan Mulote. A compulsory pre-school year for six-year-olds has been introduced to help with school-readiness. Photograph: Miikka Pirinen

Not even on outlawing school fees? “The resource will just be shifted elsewhere,” Jerrim says. “There are lots of potential unintended consequences, for example, pushing up house prices near good schools.”

In 2013 the celebrated Finnish educator Pasi Sahlberg paid a visit to Eton College, the most famous of the UK’s ancient, elite boarding schools. Once a maths and science teacher in Helsinki, Sahlberg now tours the world spreading the word about the wonders of Finnish education and advising on education reform.

“It was like going 200 years backwards in time,” Sahlberg recalls of his visit. “I remember thinking while walking the corridors of Eton and watching students there that even if I had a chance to enrol my own kids to that school I would probably say ‘no, thank you’.”

With its illustrious history, bizarre uniforms and £40,000 a year fees, Eton – which educated the current British prime minister and many before him – is a million miles from the modern egalitarianism of Finland’s schools.

Facebook Twitter Pinterest Second-grader Menni Pietiläinen reads a book after official school hours. Photograph: Miikka Pirinen

“I am often asked by people what is the most important thing I learned in school,” Sahlberg says. “I say that to learn to understand that there are different kinds of people in this world and that regardless where we come from we can be in same school and learn in same classroom. Eton boys won’t learn that in their school.”

Like Jerrim, Sahlberg is sceptical about other countries trying to simply copy the Finland model. “There are so many myths about what the Finnish system is and is not. This idea of copying has done a lot of damage.” Finland’s schools are rooted in the country’s distinctive history and culture; the population is small (5.5 million), and taxes are high.

“You can’t go to Finland and cherry-pick the things that seem to be interesting and say, ‘We want to do like Finland is doing’. It’s much more complicated than that.” He also thinks it’s unrealistic for Labour to promise to abolish private schools. “It’s come too far this whole private education thinking. It’s very hard to remove it altogether.”

It would be better, he says, for Labour to focus on strengthening the existing state sector in England, which has become fragmented through academisation and free schools. “Just abolishing something, saying private schools should be made illegal, it’s not going happen.”