Walking into a small room in a communal house in north London, I'm confronted by a poster depicting an Egyptian protester hurling himself into a line of riot shields, with a message in huge capitals: "WE WILL FIGHT, WE WILL KISS/LONDON CAIRO ROME TUNIS". Elsewhere books on radical philosophy are stacked alongside photocopied "FIGHT FOR YOUR EMA" flyers and other design scraps. I'm here to meet – on condition of anonymity – two members of the shadowy Deterritorial Support Group (DSG), who use the names Pablo and Nick, and, via Skype from somewhere outside the M25, a third whom we'll call Jamie. "I'd make you dinner, but I'm skint," apologises Pablo, as they set up the laptop. "I wasn't paid this week."

At various points DSG – named as an antithesis to the Territorial Support Group, the Met's public order riot police, and kettling specialists – will identify themselves as "Ikea anarchists", "autonomist Marxists", "humorous provocateurs", "cartoonish materialists" and an "ultra-left propaganda machine" (their official description). These tongue-in-cheek/silly labels might mark them as determined outsiders hectoring from the fringes, but they have cast a long shadow over politics in 2011, infiltrating mainstream debate via the virus-like spread of their internet memes. Since the student protests a year ago, they have become know for a stream of provocative political posters; for timely polemics about internet activists Anonymous, political policing and the Occupy movement; for sparking journalist Johann Hari's downfall; and for spreading across the global media an astonishing hoax about radical philosopher Slavoj Žižek offering his endorsement of Lady Gaga.

They are deliberately vague on the specifics, but it becomes clear that DSG comprises around 10-20 members and affiliates, all graduates in their early to mid-20s, either on the dole, still studying or precariously employed – Pablo has been working as a cleaner. In a key piece written in February by Newsnight's economics editor (and DSG fan) Paul Mason, entitled 20 Reasons It's Kicking Off Everywhere, reason number one, linking everything from the Arab Spring to Greece to Millbank, was "a new sociological type: the graduate with no future". DSG are that group at its most well-read and radical – and they have nothing to lose but their student debt.

Visit their blog and, as with any good propaganda, their visuals strike you first: classic revolutionary aesthetics reimagined for the internet age. In bold red and black, accompanied by blownup images of the Twitter "retweet" symbol and Facebook thumbs-up icon, they declaim "STRIKE/OCCUPY/RETWEET" and "EDUCATE/AGITATE/LIKE". It's both tongue-in-cheek, and deadly serious. At the eruption of the student protests this time last year, says Pablo, "we saw a lot of awful propaganda, which didn't relate to what was going on. People are embarrassed about talking about Facebook and Twitter, because it relates to their everyday life, which is stupid – it's the way we share information. Fifty years ago they'd have been talking about occupying a TV or radio station."

DSG's posters around the large trade union protests on 26 March became notorious, taking the "March for the alternative" TUC branding and subverting it to provocative effect, turning the open-palmed TUC hands into raised middle fingers, suggesting that people "occupy", "kick off", or "fuck shit up for the alternative". The posters spread virally across the internet, and were plastered on lamp-posts and walls in London. The TUC were, Pablo feels, asking to be parodied. "Their campaign was non-confrontational almost to a comical degree." The aesthetic was "very consciously decodified, without any political affiliation whatsoever. Instead of primary colours it was teal and beige and turquoise." So DSG "recodified" the TUC posters in "traditional confrontational colours of the left", red and black.

"What separates us aesthetically," continues Pablo, "is that without the specific historical and economic conditions I live under, I don't feel would be involved in this sort of thing. These are times when you have to grab the opportunity." So what would they be doing, if they were born into another age? "Probably have a mortgage or something?" Nick says. "As cartoonish materialists, the material conditions own us." Indeed, they would never have started DSG were they not unemployed, poor, and fired up by the student protests of last winter – for them, the storming of Millbank represented a kind of "year zero". Indeed, Nick admits to voting Lib Dem in May 2010, and Pablo, with a chuckle, to being a former member.

Over several hours they dispense praise for radical designers and propagandists such as Atelier Populaire, Grapus, The Designers Republic and Class War, and have harsh words for almost everyone else, including the Labour left ("2011's real utopians"), the Lib Dems ("trepanning on the brain of social democracy"), Adbusters ("hipsters are the abortion of the vanguard"), and the Trotskyist SWP ("how endearing to base your entire political outlook on a text written in 1921, under very specific conditions"). They seem equally in love with radical theorists such as Gilles Dauve, and lolcat pictures.

Their aims, they said earlier this year, are "full communism, with lulz as a transitional demand". Surely that was just a gag? "In the one hand it's completely honest," says Nick, "and on the other it's a joke in its own right, which is similar to a lot of the stuff that we do."

At times this year DSG's jokes have got slightly out of hand. In June the Murdoch tabloid the New York Post ran an astonishing story entitled "Marxist muse befriends Gaga", reporting that "the world's hippest philosopher" Slavoj Žižek was cavorting with the world's biggest pop star. As their source they quoted a long essay Žižek had written for DSG, applauding Lady Gaga's militancy, entitled Communism Knows No Monster. Except, he hadn't written it at all. The story's obvious falsehood didn't stop it being picked up by the Los Angeles Times, Vogue, Fox News and Vanity Fair. On Fox, Nick recounts. "It was established in the first two minutes it was a hoax, but they nevertheless spent a further eight minutes discussing it, which is fantastic." So what did you make of Žižek's response in the Guardian Review, that "there is an anarchist leftist group here in London who hate me"? "We were heartbroken!" says Nick. "We're not anarchists, and we don't hate him! He's a great communicator, which is more than you can say about a lot of academic leftists."

Some of DSG's coups have been more serious: their discovery of Independent columnist Hari's extensive plagiarism of an old interview with the Marxist philosopher Antonio Negri escalated fast, as the rightwing press picked up the baton, and turned it into a pitch-fork. "I was just casually reading an obscure Negri text," Jamie says. "It's pretty difficult to get hold of – the only way I found it was by downloading it. You know when you're reading something and you think, 'I've seen this somewhere before'? So I started going through Hari's Independent piece and I was shocked – genuinely shocked."

In the ensuing scandal, the debate over plagiarism eclipsed DSG's original point: that radical thinkers such as Negri are routinely and deliberately misrepresented. "What's been lost," laments Jamie, "is the specific content of the discovery: a liberal journalist fabricating material about a person on the radical left, accusing him of murder, in order to smear him, and by proxy to smear radical thought.

"Journalists like Hari police the boundaries of what is acceptable thought. It's the left wing of capital, as the old anarchist critique of social democracy says." It's sad, he continues, that the politics was stripped out of the debate, but it's how our elites function: just like the TUC's timid aesthetics and bland colour schemes.

Another striking thing, given their leftist politics, is their refusal to reject the trappings of consumer capitalism. "You can't be a communist in a capitalist world," says Pablo. They shop at Tesco, they happily admit. "That's what DSG is about aesthetically as well, which is being based in your everyday life. Most people like shopping at Tesco." Same with Ikea, says Nick, pointing to a description of DSG's aesthetics as "Ikea anarchism". "I'm happy with 'Ikea anarchism', because they give reasonably good design, on the cheap, to a lot of people, and it's very popular. It's better than the alternative, which is handmade anarchism."

"Be the change you want to see in the world", goes the hippy motto. It chimes with Louise Mensch's and Theresa May's criticisms of Occupy St Paul's protesters: how can occupiers call for the end of capitalism, yet still buy coffee from Starbucks? Pablo grins. "What's really interesting about those glib rightwing reactions is, if that's really the best argument you've got, then there is no real defence.

"Four or five years ago their argument would have been: 'Capitalism has given you everything you ever needed.' Now it's: 'You're drinking coffee.' Capitalism is a relationship caused by wage labour, and you can eat as much organic food as you want, but you're not changing those fundamental relationships."

He pauses. "I think the real problem with 'be the change you want to see in the world' is the change I want to see in the world, I can't embody."

And that change involves a world that fully embraces the advances of the 20th century, not a retreat to the hills. "Thatcher exploited the fact that people wanted to buy their own home, and live in a nice place, and have a lot of nice material possessions," continues Pablo. "And that's what I want! I don't want this sort of leftist poverty, and the left in Britain needs to get over this asceticism, the idea that fighting capital means suffering behind a machine. You go along to Trotskyist events and they're arguing for the right to work – I don't want the right to work! What I'd like is to work less." Always keen to show the working behind their final answer, Jamie cites a report by the New Economics Foundation, saying that at the current level of economic output, Britain could comfortably reduce the working week to an average of 21 hours a week.

This all sounds wonderful, of course. But DSG isn't that optimistic about the imminent arrival of a new world – at the very least, it's sure change won't come from the TUC, or from Westminster. "Capital has already smashed organised labour, and now it's going to work on parliamentary democracy: across southern Europe, there's this slipping into a state of exception," Pablo says, reflecting on the recent appointments of "technocrats" to head the governments in Greece and Italy, and concern about a resurgence in fascist parties ("the fash"). "This postwar argument that capitalism and democracy go hand in hand; well maybe that was just a transition period before capitalism reaches its actual zenith, which is ... China?"

Young radicals have always pontificated about a world after capitalism: the difference for DSG, and the generation it preaches to – the children of New Labour, the internet and ubiquitous branding – is that it looks more realistic than ever before. One of the most dramatic of its posters, which reads THE POST-POLITICAL = THE MOST POLITICAL, was created in response to some older voices on the left complaining, almost nostalgically, that the August riots "weren't even political".

From the laptop, Jamie's voice pipes up – the poster is, he thinks, all that needs to be said about the riots – in a way, all that needs to be said about the age we live in. "Some people asked me what it meant, but it means exactly what it says: the post-political is the most political. It hits the nail on the head. Mainstream politics is over. It's over! It's us, capital and the fash. That's it!"