In January 2000, James Tooley, then working as a consultant for an arm of the World Bank, left his five-star hotel in Hyderabad, India, to see the Charminar, described in the guidebooks as the city's "must see" attraction. As his autorickshaw proceeded through middle-class suburbs, he was struck by the ubiquity of private schools. But the Charminar, a triumphal arch built in 1591, stands at the heart of the old city slums. And, to Tooley's surprise, the private schools didn't thin out as he passed through poorer areas. When he continued his journey on foot, deeper into the slums, "there seemed to be a private school on every street corner".

These were not, with a few exceptions, philanthropic concerns run by charities. They were private, profit-making enterprises, run by local entrepreneurs and charging rock-bottom fees to poor parents. Nor, it turned out, were they confined to Hyderabad. As Tooley went elsewhere in Africa and Asia – to Ghana, Nigeria, Kenya, even China – he found similar schools. He ventured down stinking alleyways, stepped through open sewers, tramped to remote villages. Poor parents, exasperated by the failings or even non-existence of state education, had exerted "people power" and achieved what Tooley calls "grassroots privatisation".

In nearly every case, he discovered, these schools, though they relied largely on unqualified teachers receiving minimal salaries, outperformed the state schools. Most remarkably, state education officials and aid agencies denied their very existence. Yet many schools had started at least a decade earlier and, in India, similar schools existed 200 years ago, only to be wiped out by British colonialists.

In and around Madras in the 1820s, according to documents Tooley found in London archives, a "deep-rooted and extensive" education system covered 25% of the male school-age population, a level then comparable to most European countries. Around Bombay, "hardly a village, great or small" lacked a school. Even more amazingly, Indian schools used an "economical" teaching method whereby older pupils taught younger ones. This method was supposedly invented in Britain by Andrew Bell and Joseph Lancaster. But as Tooley tells it, they plagiarised it from India.

Tooley, now professor of education at Newcastle University, tells the story in his book The Beautiful Tree – the title is from Mahatma Gandhi's metaphor for indigenous Indian schooling, which he accused the British of uprooting – first published in 2009 and just out in paperback. It is written with verve, humour and suspense. When I met Tooley in Newcastle, I said his views echoed those of the de-schooler Ivan Illich, whose work excited the western left in the 1970s. In a lecture in 2005, Tooley said that "as the market develops … education will become organically linked again into … family homes, workplaces, sports centres, town halls, reading rooms in pubs, debating chambers, book stores … but you won't see the youth ghettos we call schools and colleges".

Tooley told me Illich had indeed been an influence. At a Bristol comprehensive in the 1970s, from which he eventually dropped out without completing his A-levels, he was taught by "a radical de-schooler who started a folk club where I wrote anti-school songs". Though his parents were Conservatives, he was a lefty as a young man and once joined the Labour party. After eventually taking his A-levels privately and then a maths degree at Sussex University, he travelled to Zimbabwe to teach and to assist, of all people, Robert Mugabe, in building socialism.

Tooley, 54, is charming, jolly and generous, and nobody who knows him doubts his sincerity and his genuine enthusiasm for what are, rather ambiguously, called "low-cost private schools". Nor would anyone now seriously dispute the existence of such schools or even their frequent superiority to neighbouring state schools, though the scale of the superiority is disputed.

But some would say that as far as state education is concerned, Tooley is a dangerous character. He has been described as "the high priest of privatised education in Britain" and, by Stephen Ball, a professor at London University's Institute of Education, as "a policy entrepreneur par excellence". The Beautiful Tree misleads the reader – Tooley insists this was unintentional and blames the editors – into thinking that, in 2000, he was still a socialist by conviction who had somehow drifted into working for the World Bank and was converted in Hyderabad to the glories of private education. In fact, he was already a leading advocate of privatisation who founded the education unit at the rightwing Institute of Economic Affairs in the mid-1990s.

Though he described the Hyderabad visit as "my epiphany, when the bits of my life came together", the Damascene moment, he said, occurred much earlier at the Institute of Education in London when, during PhD studies, he read EG West's Education and the State, a sacred text for free marketeers. It argued that, long before the 1870 Education Act established compulsory state education, the majority of English children were literate, thanks to private and voluntary schools. Tooley found private schools in Hyderabad because he wanted to find them, having accepted the West thesis that, in the early 19th century, they were doing a brilliant job in England and would do so again if the state stepped aside.

Now he has become an investor in private schools, remortgaging his house and sinking his savings into schools for the poor in the developing world. He initially linked with Orient Global, founded by the New Zealand-born billionaire Richard Chandler who specialises in investing in developing economies, to work in China and India. He soon broke with Chandler, but refuses to talk about the details – except to say, in future, he will be more wary of men with Boeing 737s – and concentrated on building Omega Schools with a local partner in Ghana. The company opened its first schools in 2009, and now has 40, with 20,000 pupils. Tooley predicts 100 schools with 50,000 pupils next year.

Last year, Pearson, owner of the Financial Times and the world's biggest educational publisher, took a stake in the company, allowing it to expand throughout Ghana. Pearson's chief education adviser is Sir Michael Barber, formerly a top aide to Tony Blair and an old friend of Tooley's from when both men were teaching and building socialism in Zimbabwe.

Tooley is cagey about the business model, but says he hasn't taken any money out of the company and doesn't draw a salary. Nevertheless, he is "relaxed" about his partner becoming rich and thinks Pearson "is excited by this market". He insists that the daily fee, the equivalent of about 40p per child, is not only affordable to poor parents but no dearer than state schools. "It covers everything, including lunch, two uniforms, workbooks and a bag. The state schools charge for extras, so many parents see the costs as identical." They choose his school because it is better value, with the average pupil's reading (according to Tooley) well ahead of his or her peers in government schools.

"They see teachers arriving at the government school at 11am and leaving at 12. They see them sitting outside and not actually teaching while the children are sent on errands. In a private school, there's an owner and, if the teachers don't turn up, they'll be fired." As in the private schools he discovered, Tooley's teachers are largely unqualified and on low wages. "They are typically high school graduates. Some are saving up to go to university or doing it for idealistic reasons as I was in Zimbabwe. We create everything they need centrally – lesson plans, workbooks, exercises – and give them a three-week crash course."

Tooley believes this bargain-basement education offers the best hope for the future of the developing world. Aid agencies, he says, should switch funds to supporting such schools rather than subsidising state systems which, despite the billions poured into them, still fail.

These views are bitterly contested. Education, critics argue, should be a right, not a commodity for which parents pay. The biggest educational gains in Africa and Asia followed the spread of free public education; the future lies in spreading it further and making it better, not in propping up a private sector that can never guarantee universal coverage, equity or consistent standards and usually excludes those in the most extreme poverty. "Every dollar households spend on school fees," says Prof Keith Lewin of Sussex University's centre for international education, "is a dollar less to spend on health, clean water, food and shelter. So fee-paying private schools increase poverty directly."

An exhaustive study of the evidence, recently completed by Claire Mcloughlin, a senior research fellow in international development at Birmingham University, reports that, while rigorous studies such as Tooley's find privately educated pupils doing better than peers in government schools, even after socio-economic background is taken into account, "other [albeit fewer] studies find the opposite". The findings, Mcloughlin says, "are inconclusive".

Nevertheless, private school chains are spreading across the world. Pearson has also invested in Kenya's Bridge chain, which opens 2.5 schools a day and now has more branches than any other Kenyan business.

Tooley believes that countries such as Britain should learn from India, Ghana, Kenya and others. We, too, could have low-cost private schools if they were run commercially, as established schools such as Eton and Harrow are not. With bigger classes, more modest buildings, less experienced teachers and more technology, they could charge less than £2,000 a year per pupil.

"I don't support Michael Gove's free schools or US charter schools," he says. "I'm a purist. The government shouldn't privatise education because it will make a mess of it, as it did with the railways. I want to see private schools emerge and then the state just move aside from education."

He is unfazed when you suggest that, in a schools market, as in energy, banking, retail and a host of other markets, we would end up with a handful of big chains, some controlled by hedge funds or foreign conglomerates, spending more on sales, marketing and shareholders' dividends than on teaching children, and restricting choice rather than widening it. He says that school chains with names such as EasyLearn or Virgin Opportunity could, to parents, carry similar guarantees of quality and reliability as those of Sainsbury's or Boots. But he also says there should be and will be room (without quite explaining how) for more local school enterprises.

Fanciful ideas? Perhaps, until you think how rapidly they are spreading across the developing world and how private capital is making inroads to higher education both here and in the US. I like Tooley but, if I were a highly qualified teacher working in a publicly funded school, particularly in Newcastle ("a good place to start a low-cost private school," he says), I would be afraid of him. Very afraid.