“Phalanstery,” reads the buzzer outside the HQ of the anarchist magazine Strike! How I’m meant to work out that this is their office eludes me. I have to phone my contact to check – but that’s anarchism for you. At least I learn a new word. Phalanstery (or Phalanstère) was the name of a building designed by 19th-century philosopher Charles Fourier to house a utopian community. That’s also anarchism for you.

Setting up a meeting with Strike! has been delicate. “We find ourselves in a bit of a bind,” one of them emails me when I first get in touch. “We don’t really want to focus attention on ourselves. We want the focus to be on collective action, not prominent individuals – on the issues of exploitation and alienation, not petty acts of vandalism.”

A recent Strike! Magazine cover. Photograph: design@strikemag.org

Those “petty acts of vandalism” are another reason why setting up an interview is tricky. Strike! was in the news recently when quotes from one of its articles appeared on brightly coloured posters on London tube trains, neatly pasted over legitimate adverts the Monday after New Year, just as people were returning to work. The article, by anthropologist David Graeber, excoriated “bullshit jobs”. Sentiments like “How can one even begin to speak of dignity in labour when one secretly feels one’s job should not exist?” struck a chord, but sticking up posters on Tube trains may also constitute criminal damage, so they’ve had to tread carefully, especially since a series of anti-police adverts – based on original designs by Strike! – were plastered on bus shelters around London the previous month. “We caused the 2011 riots,” read one, mimicking the look of police adverts, “by shooting dead an unarmed civilian and then lying about it. And we got away with it.”

To secure a meeting, I agreed not to give their names. They are four young people, with ages ranging from 22 to 32. The 32-year-old, a man with a background in journalism, set up Strike! two years ago with a female designer, now 26, using his redundancy money from a job at a charity to fund the first issue. They have since taken on two female co-workers: a student and a journalist, both 22. Neither they nor anyone who contributes to the magazine, which celebrates its second birthday this month, gets paid. It is “an efficient business model” since their only costs are printing the 2,000 copies they sell by subscription, in anarchist-friendly shops and on the street. Even their premises, in Fleet Street, come free courtesy of a trust that offers a home to radical organisations. “We are,” they point out proudly, “the last paper in Fleet Street.” The traditional home of journalists is now inhabited by bankers, lawyers and other practitioners of what Graeber would certainly describe as bullshit jobs.

Published in November, issue eight of Strike! featured an article celebrating the “radical print revolution” that has brought about an unlikely flowering of new publications. Strike! – well-produced and currently running an exhibition of its artwork in a north London hairdressers – sees itself as part of that revolution. But why bother going to the trouble of publishing a large-format print magazine in our supposedly digital age?

“I had experience of writing political blogs,” says the 32-year-old. “Obviously the internet has an infinite audience. But that sometimes means it has an audience of nobody. That has a consequence for quality: because they’re infinitely editable, people think, ‘Just put that up and we can go back to it later.’ With print, there’s a lot of quality control.” The female designer adds: “It makes you think very strongly about what you’re going to put in because we don’t have a lot of space.”

One of the spoof job adverts that appeared after New Year on London tube trains.

What they put in tends to be a mix of academic articles by leftwing thinkers such as Graeber, Slavoj Žižek, Danny Dorling and Nina Power; more whimsical pieces like the recent Anarchist Guide to Christmas (praising Santa’s workshops as “not-for-profit, craft-based and run on communal lines”); how-to guides to such anarchist activities as flyposting (“wear the internationally acclaimed cloak of invisibility more commonly known as hi-vis”); and artwork by artists such as Peter Kennard, co-creator of the infamous spoof selfie of Tony Blair in front of Iraq ablaze. Strike! sells for £2 – the collective unanarchically doubled the price when they moved from quarterly to bi-monthly publication last July – and is now self-funding.

They prefer not to describe themselves as an anarchist publication, opting to say instead that it is “run on anarchist principles”: non-hierarchical and non-profit-making. Each of the four do something else in their non-Strike! lives: the designer works for a printing cooperative; the two writers do freelance journalism; the student, as well as studying for a masters degree, teaches dance. But they insist their commitment to changing society doesn’t stop when they leave Strike!

In issue two (“the sedition issue”), they ran a piece by former New York Times foreign correspondent Daniel Simpson decrying the conformism of “big media”. They share his misgivings: it’s another reason why fixing an interview with them had to be negotiated. “We’re enormously mistrustful of mainstream media,” they emailed. “Obviously we are, or we’d all be working for mainstream media, not putting out the alternative.”

The group believes anarchist actions – direct efforts to initiate change – are as important as words. Nevertheless, they distance themselves from the two recent flyposter campaigns on bus shelters and on the underground. “We had no part in the actions beyond the original designs in the case of the police posters and commissioning David’s article in the case of the tube takeover.” They say the posters were the work of an anarchist organisation called the Special Patrol Group and admit to knowing at least one of its members. “One person got in touch to ask if they could use the quotes for the tube posters,” says the 32-year-old. It’s a nice touch: an anarchist planning a direct action was fretting about copyright infringement.

Another spoof bus ad based on a design by Strike! magazine. Photograph: design@strikemag.org

A Greek anarchist friend of mine dismisses Strike! as an example of “anarcho-populism”: the general growth of leftwing protest movements that have followed the crash of 2007-08. True anarchism, he says, sought to overthrow the existing system of state power and capitalist economic structures; anarcho-populism, with Russell Brand as its celebrity symbol, was closer to a fashion statement. Strike! dismiss this view, arguing that Occupy and the other organisations spawned by the crash were serious, hard-edged and viciously repressed by the state. More surprisingly, perhaps, they think Brand is a good thing. “Russell Brand, to his credit, often says, ‘Look at this campaign, look at this thing, please look over there’,” says the designer. “But all the media want to do is look at him and film him.”

The young writer blames mainstream media more than Brand. “Activism existed before Russell Brand,” she says, “but the media think that, if a celebrity has done something, that gives you permission to write about it. Brand’s used his celebrity very well, because he understands that the media needs a name before they can have a conversation about an issue. But there’s so much more activism beyond Russell Brand that the media doesn’t see.”

Where, I ask, is the magazine going? The flyposter campaigns have brought them attention. This article may boost them further. Is there a danger they will become victims of their own success, anarchists who are worth a bomb? “There’s no game plan,” says the designer. “It’s growing, but it’s not target-driven. All that comes from capitalist discourse. We’re just making something we think is good and getting better. That’s all there is to it.”

• Artwork from Strike! is at Flaxon Ptootch salon and gallery, London NW5, until 10 February.