In the last week alone, members of Extinction Rebellion have been described as ecomaniacs (Daily Mail), ecoradicals ignoring our economic doom (Times), dangerous and a bloody mess (Daily Telegraph). They have been accused of “pulling 83,000 officers away from their normal duties” according to the police and costing Scotland Yard £16m. In London last week, dressed in funereal black, rebels tried to paint the Treasury red using 1,800 litres of fake blood and an old fire engine with a sign reading “stop funding climate death”.

While its actions may seem controversial in some quarters, Extinction Rebellion’s rise and influence have undoubtedly been extraordinary, galvanising young and old across party lines. Last October, the journalist and activist George Monbiot introduced the group in the national press, a homegrown movement “devoted to disruptive, non-violent disobedience in protest against ecological collapse”. The hope was to turn a national uprising into an international one by March. In fewer than 12 months, Extinction Rebellion has become the fastest-growing environmental organisation in the world.

“We have seen protest movements on climate change before, but they haven’t attracted anywhere near as many people or had as much impact,” said Clare Saunders, professor in environmental politics at Exeter University. “For the first time, you have ordinary people engaging with radical action. It’s unique – I can’t think of any [protest movement] historically happening in that way.”

There are now an estimated 485 Extinction Rebellion affiliates across the globe and, over the next fortnight, they are promising to shut down 60 cities, including London, New York, Buenos Aires, Sydney, Cape Town and Mumbai. Government buildings, airports and financial districts will all be targeted with protests aiming for maximum disruption to provoke urgent political action. In a bid to pre-empt the action, on Saturday police raided a warehouse in south London and arrested nine activists, charging them with conspiracy to cause a public nuisance and obstruct the highway.

People think going vegan and recycling will stop climate change – it won’t. Government has to act Jules Bywater, Cardiff protester

How did they come so far, so quickly? The Observer has watched the movement at work in city centres, at festivals and meetings across the UK to try to find out.

“It’s maintaining hope in people because people are feeling so worn out by the inaction,” said Steven from Cardiff, who joined the summer uprising in the city in July. When the Observer met him, he and his partner Clare were sitting on the green outside the town hall, where Extinction Rebellion had set up base with a boat, an impromptu campsite and stalls serving free food to the public. “I’m not sure the damage to the planet is irreversible at this point – all the science points that way, it’s grim reading – but this is pricking people’s ears up more than any other group, and that can only be a good thing.”

The Cardiff rebellion, staged over three days, saw a massive police presence deployed as a procession of families and activists marched through the city centre. Jules Bywater, a builder of eco-homes, had travelled from Powys to join the action. “People think going vegan, banning single-use plastic and recycling will stop climate change – it won’t. Government has to act, and it’s on us to cause these disruptions to force them to. This has to be a mass movement.”

Alice Taherzadeh, a PhD student and one of the key organisers, was buoyant but exhausted. “We had less than a month to get this together,” she said. As a decentralised organisation, XR, as it is known, claims no hierarchy: it is open to all and operates a “regenerative culture”.

In theory, this means responsibility and workload is designed to be a shared, collaborative effort with heavy emphasis on community, and mental and physical wellbeing. In practice, a hierarchy does still exist, albeit under the surface, where some people are in the loop, go to the pub together and have access to the latest comings and goings from HQ, while others volunteer more on the periphery. Still, to witness it across uprisings in London in the spring, and across the UK over the summer at festivals and meetings, the spirit of XR is warm and often moving. The culture it has fostered also allows for a surprising amount of internal criticism of its founders, Roger Hallam and Gail Bradbrook.

“The movement and its principles are far bigger than both of them; they’re not these messianic figures they’re made out to be,” said Taherzadeh wearily.

Hallam is a former organic farmer who went on to study civil disobedience at King’s College London after “the weather went weird” and caused his business to fail. He formed XR with Bradbrook, an academic involved with Occupy and anti-fracking protests, and the two have championed non-violent resistance and civil disobedience. Their methods, including advocating a shutdown of Heathrow, have been effective but divisive.

“I don’t think Roger is the best spokesperson, necessarily,” said Taherzadeh. “Some of his tactics – drones at Heathrow for instance – have caused huge conflict. But the unity in the movement exists because of the three core demands: get government to tell the truth, get government to act now, and to draw up citizens’ assemblies.”

There is a quiet desperation and sometimes despair at how hard and possibly futile any personal effort seems in the face of the climate crisis. But those touched by Extinction Rebellion find it impossible to ignore the ways in which they are contributing to global heating. This isn’t just about recycling, switching to bamboo toothbrushes and buying in bulk; people are re-insulating their homes, dramatically scaling back family holidays to eradicate air travel and, in increasing numbers, deciding not to have children at all.

The movement’s Summer Uprising occupied Bristol city centre in July. Photograph: Miriam Quick

“I’m scared of my own future,” said Dahlia, a 20-year-old student at the Bristol uprising. “How could anyone think about having kids now? It’s not even just about the carbon footprint and population growth … what kind of world are you thinking they’re going to live in?”

The summer rebellion in Bristol took over the city centre and installed a pink boat and white gazebos on the Bristol Bridge. Billy Bragg performed, and hundreds joined talks and workshops explaining how activism works, how to get involved and what legal rights might be for protesters who get arrested.

But it isn’t just for the loud and energetic, or those willing to go to prison for the cause. At a crafting session in Totnes, a dozen women quietly work on their “craftivist” skills; almost every one joined XR in the last few months, and they volunteer as behind-the-scenes environmentalists making flags, banners and the like. Some are put off by the noise and physical toll of being on the streets; others describe themselves as too introverted to protest in that way. Yet the zeal is still palpable.

“We’ve just spent our family holiday in the UK,” said Sarah Strachan. “Once you learn about it, read up on it … I can’t countenance how we could fly somewhere. You just can’t, and it does consume you. But how can you not try?”

Strachan works as an artist in Totnes and lives with her partner and their son and daughter. She began making tiny doll figures of the school strikers last year, as a casual distraction from the puppets she was already crafting in her home studio. Nine months ago, she had barely heard of Extinction Rebellion, but in the summer she joined the rebellion in Bristol and is working for the next one.

At home and at work, the climate crisis has engulfed her; last month, Ghost, her biggest piece yet, went on display in a local church and is set to tour next year. In it, she assembled 1,000 donated and secondhand toy plastic animals, painted them white and installed them as an eerie-looking herd. “It came from the horrible realisation that these plastic animals will be around for hundreds of years and will outlive some, if not all, of the animals they’re modelled on. How have we let this happen?”

Extinction Rebellion’s success goes beyond the efforts of its volunteers, known as rebels, who are determined, as they are often heard to say, to be on the right side of history. Business has also been under by pressure to respond to a shift in public opinion. A sustainable building designer, who asked not to give his name, said: “Extinction Rebellion have had a tangible impact. Would things be moving as fast otherwise? Shortly after [the spring rebellion], the UK government became the first to pledge to cut [greenhouse gas emissions] to almost zero by 2050. Every architectural and engineering practice has been or should be trying to work out how net-zero carbon can be delivered.”

Since XR’s launch, the architecture, engineering and construction industries have all declared a climate emergency, committing to work together to reduce emissions and work in a sustainable fashion. At least 232 councils out of 408 across the UK have followed suit. Possibly as a gesture, 15 universities including Bristol, Newcastle, Manchester and Goldsmiths have done the same, as has the UK music industry and “Culture”, an umbrella group of more than 50 organisations and artists. The National Theatre and the Royal Shakespeare Company have severed financial ties with Shell and BP respectively. It remains to be seen what all this activity translates into: while some organisations have simply adopted the vernacular, many are actively working to force change in their industries. Either way, Extinction Rebellion has been credited as a catalyst – albeit not one without criticism within the environmental movement.

Extinction Rebellion’s Rebel Rebel stage at this year’s Bluedot festival in Cheshire. Photograph: Tomm Morton

“Some grassroots groups hate them because they’re not anti-capitalist [enough], they are for-profit and pro-arrest,” said one anonymous worker from a major environmental organisation. “The pro bono lawyers’ group Green and Black Cross [GBC] have been working with activists for decades and they’ve taken on so much casework for XR – for free, despite them raising so much money and the core crew being paid – that it’s taken away from other crucial activism work.”

Earlier in the summer, GBC ended its relationship with XR, citing “serious concerns about the safety of both legal observers and those taking part in action associated with Extinction Rebellion”. Meanwhile, Wretched of the Earth, “a grassroots collective for indigenous, black, brown and diaspora groups and individuals demanding climate justice”, wrote an open letter to XR asking that their voices and experiences not be erased from the fight.

“Making people feel guilty without offering anything else is a waste,” said Sylvia Kingston on the bridge at the Bristol rebellion, when asked whether XR could do better to engage marginalised communities. She described herself as a pensioner standing up for my grandchildren” who, like so many others at XR gatherings, claimed she wasn’t an activist, “or a hippy”, or particularly on the left. “You want people to feel energised, which is why things like this are so necessary. Perpetual despair will burn you out … My generation, people like me, can afford to be here – and they should be.”

While the momentum behind XR shows no sign of slowing yet, answers for what happens next aren’t in easy supply. “We’re not claiming to have solutions,” said Bywater. “There are experts for that, there is a great deal of technology, there is plenty of knowledge to be harnessed. What we’re doing is telling government to listen to that. To act. And that pressure can only come from more of us being here.”

It’s seen as good that minds are being changed, even if XR’s demands are not always perceived as realistic. “They must know what they’re asking for – net zero carbon by 2025 – is virtually impossible. I guess their statement is a calculated risk,” said the building designer.

Saunders agreed. “There are very good reasons that Greenpeace and WWF will have to publicly distance themselves from XR – if you have more radical actions out there, your organisation’s demands might seem reasonable and palatable to a government taking steps to act.”