Every Saturday morning at 9am sharp a little bit of anarchy breaks out across the country. This being Britain, it happens, naturally enough, in our parks. Not that it’s billed as such. It’s meant to be a 5km run, which is why at Richmond Park in south-west London this morning the grass is carpeted with well over 400 people in sports gear. But it has none of the intensity you’d expect at a track or even on a gym treadmill. One woman tugs balloons, to celebrate her 100th run; others prepare to push baby buggies or keep pace with their dogs. Although supported by the charity Parkrun, this and the 559 other events across the UK set to start in a few minutes are entirely self-organised.

What they share is an ethos. Parkruns are free to all, and all are treated equally. No hierarchy intrudes between the hares and the tortoises, the old-timers and the debs. Members volunteer to mark the course or keep time or to aid stragglers. So early this morning, as the weekend still brims with promise, on these hectares of parkland owned by the Queen, a little anarchist world briefly comes into focus. One devoid of government nagging or corporate profiteering, but reliant instead on mutual aid and human kindness.

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“It is the new church,” says Karen Weir, who started the Richmond parkrun in 2006. The former City management consultant would give up 10 hours a week just to ensure Saturdays went smoothly for everyone else. “The idea of the community has broken down. People don’t go to church any more. But here, you come together with a load of people – and you feel embedded in the local area.”

Even though he’s not running today, Gary Wimbledon is here to meet friends. When the 41-year-old first came with his brother, Steve, back in 2011, he’d never even run for a bus because, being partially blind, he explained: “I’d fall over.” That first go was grindingly hard, but then came the finish line: “Never before have I had people cheering me on. And they were cheering my name! Just thinking about it, I can feel the hairs on the back of my neck stand up.”

When he started, Wimbledon carried an extra 60 kilos. Running in Richmond Park helped sort that out, and his depression. A few years into the new pastime he got married – and celebrated with a group parkrun on his wedding day. Now he’s heading for his third marathon.

It’s almost nine, and a man hops on to a tree stump to brief us. He welcomes first-timers, and we applaud the volunteers and whoop a husband and wife about to start their joint 250th run. Then it is announced that a regular, Fred Croft, died of cancer the previous Tuesday. Taking the stump, his son tells the crowd that Fred had always loved running in this park, “the varying seasons, the views, the deer”. Most of all, he “talked about parkrun as his family”. James quotes from a race report his dad wrote of the very course we are to run – a fragment from the Old English poem The Battle of Maldon: “Our spirits must be firmer, our hearts stronger / And our courage greater as our strength diminishes.” Heads bow, before the shout goes up: “Let’s run!”

Facebook Twitter Pinterest ‘Never an elite runner, Paul Sinton-Hewitt had by accident become a world-class innovator.’ Photograph: Alecsandra Raluca Dragoi/The Guardian

Here to break me in for my first parkrun is the man who started it all. By October 2004, Paul Sinton-Hewitt was “in a bad way”. Sacked from his marketing job, he’d also suffered a training injury that ended any hopes of doing a marathon. Isolated and low, his response was “to give something back”: to organise a weekly run around the local park in nearby Teddington, where he would time friends’ runs, before they all had a fry-up. He bought a bag of steel tokens from Halfords, stamped them with numbers and after each race would sit in a Caffè Nero, typing up the results. That was fine at first, when only 13 runners would pitch up. But no one else was putting on a regular free 5k run, and as numbers grew friends would fret. Sinton-Hewitt had no permission from the park, no insurance: he was heading for a mishap of Wile E Coyote proportions.

Both “altruistic” and “a complete bugger”, Sinton-Hewitt justified every breach by pointing to the spirit of the races. Free and fun, what harm were they doing? Only now it was no longer diehards running, but mothers with kids – and they were clamouring for runs to be put on in other parks. He had both a big success and a stonking headache.

Never an elite runner, Sinton-Hewitt had by accident become a world-class innovator. Today Parkrun is the largest running event on the planet, with more than 1,600 events. The London Marathon may attract the wacky costumes and the BBC scheduling, but last April not many more than 40,000 people finished it – and that was a record. In one good weekend, Parkrun’s adult and junior events pull in more than 235,000 participants around the world; within five years that’s expected to hit a million.

Innovation is one of the most overused words in business, drizzled across both gold and bullshit. When Subway announced a couple of weeks ago that market research would help it to – gasp! – tweak its menu, it said: “Global innovation is key to driving our brand forward, and we are disrupting the way we’ve traditionally managed the process.”

When Sports Direct featured this summer in a list of international shopping chains, it rushed out a press release highlighting the “top five list of global innovative retailers”, with quotes from somebody called the “head of elevation”. That Marks & Spencer cauliflower steak? You just know that some ideas meeting at head office signed it off using the i-word.

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For the right, innovation is a private sector virtue – one that you and I must encourage by paying a lot of money. Last tax year, businesses claimed tax relief on research and development worth £3bn, according to estimates from Her Majesty’s Revenue & Customs. That is more than Britain spends each year on prisons, and big companies do not even have to pay corporation tax to qualify. Then there are the special handouts, such as the £5m George Osborne hoped to collar for AstraZeneca’s Alderley Park research centre in Cheshire, just a few months before the pharmaceutical giant closed it down.

Others argue that it’s the government that enables radical innovation. Think of space programmes and arms manufacturing, or look at your smartphone in which, as the economist Mariana Mazzucato observes, all the smartest bits were first developed in US government labs.

Where both left and right agree is that innovation is about lab coats and metal-bashing, Silicon Valley and science. In other words, it looks nothing like my slight and softly spoken running partner, who is even now encouraging the two women behind us to overtake.

In those early years, Sinton-Hewitt had to write his own software, get permission from park officials who’d never heard of such a thing, devise an entire ethos for this movement he’d started. “I wanted to disrupt things, I wanted to take on all the people making so much money out of running.” In his more lucid moments, Elon Musk might say something similar – except, unlike other innovators, Sinton-Hewitt wasn’t seeking profit, or on a government payroll.

Parkrun started in the same year as Facebook, and Sinton-Hewitt could by now be sitting on a mountain of money to rival Mark Zuckerberg’s. But he has what the organisation’s chief executive, Nick Pearson, describes as “the strongest moral code of anybody I’ve ever come across”. When I ask where that comes from, Sinton-Hewitt pauses and coughs that it’s a long story.

Born in Zimbabwe, but raised in South Africa, he was put in a home at five after his parents split. He was tiny – “until I was about 16 I weighed only 60lb” – and was beaten and bullied by the other boys. They hanged him from his neck, slashed him from ear to ear, and threw darts at his back. “You were never allowed to show emotion” – so at first he appeared calm and driven, but in 1995, a few years after coming to Britain, he had a breakdown. It is from those experiences that he traces the ethic that underpins Parkrun: “I treat everyone as I would treat myself; give everyone the right to do what they want.”

Facebook Twitter Pinterest ‘Members volunteer to mark the course or keep time or to aid stragglers.’ Photograph: Alecsandra Raluca Dragoi/The Guardian

The status we give people like Musk and James Dyson has long historical roots. We might trace them back to 1911, and a book written by an Austrian economist sometimes called “the prophet of innovation”. Joseph Schumpeter was just 28 when he published The Theory of Economic Development, but its arguments are made with bone-rattling certainty. When it came to how innovation happens, he saw a hierarchy: “It is … the producer who as a rule initiates economic change, and consumers are educated by him if necessary; they are, as it were, taught to want new things.”

A century later, innovation no longer inevitably rolls downhill, nor does change always come from the centre. If you want to read up on a subject right now, you’ll probably go to the fifth most visited website in the world, Wikipedia. It has just 300 staff and contractors but tens of thousands of unpaid users who write and edit its pages. By comparison, Yahoo! – the sixth most popular website – still has 8,600 full-time staff.

If you want to get rid of your old table or cot, you might advertise it on your local Freecycle board. The world’s largest nonprofit recycling network, Freecycle has 5,000 gifting groups with 9.4 million members in 110 countries, including the Palestinian Authority. The global HQ for this vast operation is in Tucscon, Arizona, and has a grand total of two employees, including the chief executive. (They share the office with two other nonprofits, and if you ring, the CEO has to go outside so as not to disturb anyone.) They rely on 2,000 or so moderators, who run their boards for their communities for free.

And if you fancy jogging 5km next Saturday, you might go on a parkrun, whose core organisation is just 23 people working on an island in the Thames, in an office reached by walking through a boat yard. The only reason those runs happen is because of the 1.1m hours given by Karen Weir and other volunteers around the world over the past 12 months – work that won’t show up in the GDP data because no money changes hands.

“I know what it means to have targets and to sell. I get all that,” says Sinton-Hewitt. “But there is another economy here. An economy of helping people be the best they can be, to change their lives and to grow as individuals.”

Facebook Twitter Pinterest ‘Parkrun started in the same year as Facebook.’ Photograph: Alecsandra Raluca Dragoi/The Guardian

Wikipedia and Parkrun are both examples of “people’s innovation”, according to Steve Flowers at the University of Kent’s business school. They’re driven by users rather than producers, by volunteers rather than professionals; they’re horizontal rather than hierarchical, and they’re not primarily about making money. What drives these citizen innovators isn’t pay, but purpose: to have fun, gain work experience or just help others. This is an inversion of how we have come to think of work – it is more the gentle anarchism that you see in your local park every Saturday.

Flowers sees examples of this spirit everywhere, from open-source software to the reviews posted on TripAdvisor to the way games-maker Valve encourages users to modify its software. “It’s the invisible industrial revolution,” he says. “It’s hiding in plain sight, and once you see it, it totally changes the way you look at innovation today.”

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People’s innovation may even be bigger than the formal innovation economy. At Massachusetts Institute of Technology, Eric von Hippel carried out surveys in six developed countries, from the UK and US to South Korea and Finland. He found a total of 24.4 million “consumer innovators”, doing everything from modifying their coats to carry their babies securely, to establishing a GPS system to recover lost house keys. The UK has the single largest proportion of consumer innovators: more than 6% of all adults, or nearly 3 million people.

In his book Postcapitalism, Paul Mason writes with persuasive urgency about how this bottom-up economics could topple our existing order. Yet in the shorter run it may not challenge capitalism, but sit alongside it. You wouldn’t want a bunch of enthusiasts to design your local nuclear power station – but you might welcome their thoughts on how to reform social care reform.

At Sheffield University, Richard Jones points out that drug companies have spent tens of billions over decades on a cure for Alzheimer’s. The success rate so far has been zero. “For at least the next decade or two, practical advances to mitigate the condition are as likely to come from the informal innovation of patients and their carers and we ought to be doing much more to support that.”

Just as Gary Wimbledon promised, we are greeted with cheers at the finishing line. Sinton-Hewitt kindly refrains from letting on how much harm I have done to his run record. The number one thing sceptics ask him about parkrun is “Where’s the trick?”. “They think it’s too good to be true, but right from the beginning I decided this was going to be a beautiful, pure enterprise. There would never be a trick.”

• Aditya Chakrabortty is a Guardian columnist and senior economics commentator

• This article was amended on 29 August 2018. An earlier version said that Parkrun had more than 400 events; that figure is more like 1,600. In addition, the 235,000 adults and juniors taking part on a good weekend, are from around the world, not just in the UK as an earlier version suggested.

