Pussy Riot aren't just on tour. They're on the run.

When we meet in a secret location in central London, they make it clear that this interview is on condition of anonymity. The Russian punk-feminist protest group, two of whose members are currently travelling the world, talking to activists and journalists and raising support for their band-mates in prison, are wanted by their government, who have branded them extremists for their stand against religious patriarchy and the Putin regime. It will be illegal to read or share this article in Russia.

“There’s a media war in our country,” says the one who, today, is calling herself 'Serafima', whispering painfully through a sore throat. Since three members of the group, Yekaterina Samutsevich, Maria Alyokhina and Nadya Tolokonnikova, were tried and sent to labour camps last year, Pussy Riot has been attacked in almost every press outlet in Russia. The international outcry on their behalf goes unmarked. “Katya did not realise there was so much support until she was released. When we were in Russia, we didn’t fully understand, but now we see there truly is huge support,” says Serafima. She asks for a translation of a German proverb she knows: “Nobody is a prophet in their own country.”

Because of the very real danger that these young women will be arrested when they go back to Russia, every journalist who speaks to them must promise to reveal no identifying details. We swear to conceal not only their names, but their ages, where precisely they’ve travelled, and any physical description whatsoever. I can tell you that two members of the Pussy Riot are moving from country to country, talking to activists and journalists and raising support for their fellow band-members in prison. But there’s is so much I can't tell you. I can't tell you whether they wear their hair short and blonde or long and dark; I can't tell you if they’re six-foot hardass rock chicks in ripped jeans or slight, nervous schoolgirls. I can't tell you whether the girl curled in a hard red armchair in the lobby of a nondescript London office block, three off-key chords and thousands of miles from home, is a stranger or your lost little sister. What I can tell you is that she looks tired.

They both look tired. Serafima is pale and rasping and has a nasty-sounding cough which almost prevents her from speaking. They both look ill and drawn and worn-out; somebody's nan might tell them they look a bit peaky and ought to go to bed with some hot ribena. That's not an option, though: Pussy Riot have work to do, before they move on to the next city, and there’s almost nothing any of us can do to make it easier. In the end, I offer Schumacher a multivitamin. I pop two out of the foil packet and take one myself, because if I were Pussy Riot I wouldn't accept huge orange pills from strangers, even if they do come in a jolly box promising that they can keep a narcoleptic elephant awake for a week.

These girls are young. Very young. For their safety, I can’t say how young, but imagine how young you think they might be. Are you imagining it? They’re about five years younger than that. When they arrived I wondered, for a second, who let a couple of moody work experience kids into a clandestine meeting.

I had read their interviews, seen the court transcripts of last year's show trials, gone to protests where students in home-made masks yelled out solidarity slogans in truly awful Russian, but I wasn’t prepared for this. Not for this frontless vulnerability, this sudden reminder that behind the bright balaclavas are real bodies that get tired and sick, real people who can still have everything taken away from them.

This is how media activism works, when it’s done well. You get to see the flash and dazzle of protest, but you don't often get to see the toll exacted from individuals, the energy and courage it takes to keep going, day after day, when you're being attacked in the press and hunted by police. The younger of the two, 'Shumacher', closes her eyes in the armchair and doesn't talk to anybody, grabbing ten minutes of sleep before she has to answer more of our questions. Some Russians have a saying: “A person who smiles for no reason is a fool.” Pussy Riot are not fools.

Serafima smiles just once, when asked to describe the performance in Christ the Saviour Church in central Moscow of the song “Punk Prayer - Virgin Mary, Drive Putin Out!”, which got three of her bandmates jailed for ‘hooliganism’. She can’t divulge whether she was personally involved in the stunt. “It was designed as a maximal expression of freedom of speech,” she says, because of the iconic location of Christ the Saviour and its close connections with the political establishment. It was the biggest “fuck you” to the Russian elite that five girls could get away with. Except that they didn’t.

Since the trials, a smorgasbord of new legislation, informally known as the Pussy Riot laws, have been put into place in Russia to clamp down on the group and anyone who might try to imitate their art-protests. You can’t cover your face in public, and the laws against ‘offending religious sensibilities’ have been tightened in a way that suggests Jesus isn’t the one who’s worried. In addition, distribution and discussion of Pussy Riot’s protests is strictly forbidden. Their websites have been attacked, people have been prosecuted for making tshirts with their image, and videos of four of their impromptu concerts have been declared extremist, meaning that it is illegal to possess them in Russia. It is also illegal for any Russian citizen to criticise the administration to a foreign journalist. That’s what Pussy Riot have been doing for the past week and a half, and it’s what they’re doing right now, sitting at the end of a bare white table in a bare white room clutching coffee mugs and daring us to ask their names.

And then there’s the cultural backlash - including sexist attacks on what Pussy Riot stand for. "The simplest example is the idea that there’s a [male] producer behind us, or that we must be being paid by foreign governments - nobody can imagine that women themselves are expressing their opinions!" says Schumacher.

"In the Russian mass media they're saying we're stupid girls, not able to think. Among the orthodox believers, in the media, they tell us to stay at home, do cooking, give birth to children," says Schumacher. "And Masha and Nadya are attacked for not fulfilling their roles as mothers." This last is particularly cruel, because not only is it the Russian state that placed Masha and Nadya in Labour camps far from their children, but both have been denied the usual clemency that allows mothers of young children to receive suspended sentences.

Both women, who have been named "prisoners of conscience" by Amnesty International, were denied early release this spring, and the group is now preparing to take the appeal to the highest court in the land after continued hunger strikes put Masha in danger of her life.

In countries where Pussy Riot's videos are uncensored, you can watch them light flares and thrash guitars on the rooftop of a Moscow Detention Center, pounding out a song against the corrupt judicial system which would shortly be pursuing them, too. Their acid-bright tights and face masks stand out against the drab, cold winter like a chemical spill on snow, like something from the old days of ideological certainty seeping through to contaminate the spotless surface of the New Russia. Pussy Riot are a problem. Putin’s government would like to make that problem disappear.

A journalist from the Telegraph asks if the girls consider themselves primarily activists or musicians. “Artists,” replies Shumacher, in English, cutting off the question. They are artists first, “feminist artists,” working within a long tradition of women’s political art; they cite Riot Grrl and Oi! punk as influences, but also feminist writers and activists like Alexandra Kollontai and Simone de Beauvoir. The group was formed in 2011 as an offshoot of the performance art collective Voina, and it is clear that Pussy Riot are not just a punk band.

Instead, they are the idea of a punk band. They don’t release albums or go on performance tours; they have no interest in being entertainers. They are the idea of a girl with a guitar screaming in a church, and in today’s Russia that idea is frightening enough to initiate the kind of cultural clampdown that gives the lie to the illusion of a state at peace with itself. That was the point. “It is not three singers from Pussy Riot who are on trial,” said Nadya Tolokonnikova in her closing statement to the court. “If that were the case, what’s happening would be totally insignificant. It is the entire state system of the Russian Federation which is on trial.”

“There are two reasons why we frighten people,” says Schumacher, popping a chocolate biscuit into her mouth. “The first thing is that we’re a feminist, female group with no men connected to it, and the second is that we don’t have leaders.

“These two aspects, the structure that has no leaders and the emphasis on women, these are strongly connected. Russia has always linked the idea of leadership with some man or other, who can control things, and control women. A woman’s group with no leaders… this activism comes from a place people do not recognise, and sets itself up against the structures of power.”

The insistence on anonymity isn't just to protect individual group members from persecution. Even before the backlash began in earnest, Pussy Riot only ever gave interviews using nicknames, pursuing an image of memetic militancy: without names or leaders, anyone could be Pussy Riot. The trials of Nadya, Katya and Masha forcibly removed some that anonymity, but they have spoken out from jail declaring their willingness to see others continue the work.

Allergy to leadership and hierarchy has been a defining feature of the new youth protest movements that erupted around the world in 2010 and 2011. It's not just Pussy Riot with their bright balaclavas. It's the Arab Spring and Occupy with their horizontal, networked organisation systems. It’s the black bloc face-rag, the grinning Guy Fawkes masks on the front lines of riots and in occupied squares in Cairo, Tunis, Athens, London and, this week, in Istanbul and Sao Paulo. Nor is it only Russian protesters who now risk arrest if they cover their faces - new laws in Britain and the United States mean that if you go to a protest in a you could well face what Schumacher delicately describes as “intimate problems with the authorities.” The iconography of Pussy Riot is infectious and easy to appropriate because it works in the way that resistance works in a post-ideological age where art moves faster than organisation and repressive regimes can be shaken by irreverent protest memes, bright colours and bravery.

And, of course, it’s a girl thing. Every sexist society, including this one, fosters an image of women as basically interchangeable. Underneath the makeup, girls are all the same, aren’t we, with the same petty problems and weak, willing bodies. Pussy Riot take the image of modern womanhood as a faceless smile, repeated endlessly, and turn it back on us as a scream.

“The idea of women liberating themselves, speaking out and acting out against Putin and other forms of power is something that appears strange,” she explains, “It’s an attempt to transform the role of women, who are seen from the conservative viewpoint as people who have to behave, have to be subservient, have to be as soft as possible, as giving as possible.” It upsets people. The name upsets people. Broadcasters have trouble pronouncing it; parents purse their lips. And that’s the point, too. “People ask us all the time, which is more important, politics or feminism, and for us politics and feminism are one and the same thing.”

So. Here's how you make a balaclava out of old stockings. Cut a length off a really thick pair, preferably in day-glo pink or blue or green, and pull it over your head to work out where the eye and mouth sockets go. Snip little holes with a pair of kitchen scissors; pull them apart with your fingers. Bear in mind that if you go outside like this, you may be breaking the law in several countries, including this one. Put on your homemade neon balaclava. Now go and start an oppositional art revolution.

It’s what Pussy Riot want you to do. Really. Right now, it’s extremely difficult for the six group members who are still free to organise protests: they want their punk-feminist, anti-authoritarian message to spread around the world, and they want people to interpret it in their own way. “We’re open-source,” says Serafima. Throughout the entire interview, it’s the only thing she says in English.

“In travelling, we have understood that this isn’t just about Pussy Riot, but about a broader movement – this is very important, this is a wonderful discovery,” says Schumacher. “We met people from Occupy Wall Street and Occupy Sandy in New York, and we agree with what they’re doing. It turns out that at we inspired people, and now we are inspired ourselves. This is really key, because any living person can become Pussy Riot, if they support the ideas. We support third wave feminism, and we want to bring that wave to a finish,”.

“It’s like when Marcel Duchamp posed the question of ‘what is art?’” says Serafima softly- her throat still hurts, and she’s trying to talk through it, even though speaking is so difficult. Speaking is always difficult. “I reckon that we asked a similar question – it just takes time for everybody to understand.” Duchamp didn’t have much time for women, but he did say that “art is either plagiarism or revolution.” Pussy Riot are originals. Their manifesto is a call to action - "we are open-source-extremists, the feminist virus infecting your thoughts." In a time of bland hegemony, that takes unbelievable guts.