The protest has become a network of mutual support for the lost and destitute.

The Bank of Ideas is almost empty. It's midnight, and on the roof of London's financial district a serious discussion about the future of the Occupy movement has been interrupted to allow two stray humans to chase after one stray cat.

"We found him in a scrapyard," says a young man called Spiral, cuddling the rescued ginger tom into his hoodie. Spiral is homeless, having left Essex to live in the London occupations last October. "He didn't seem to have any owners, so now we all take care of him," Spiral says. He's talking about the cat, which purrs like a happy engine as more dart-eyed young people approach to offer it some of their dinner -- homemade vegetable soup supplemented by hunks of fish they found in a skip.

Three months on, this is what the Occupy movement looks like: a network of mutual support for the lost and destitute, with anti-capitalist overtones. The Bank of Ideas, an abandoned building owned by the Swiss banking giant UBS and transformed into a space for art sessions, lectures and late-night discussion on the future of the free market, is one of four sites squatted by London's branch of the movement. The occupations began with the encampment on the steps of St Paul's Cathedral, which has just lost its battle against eviction at the Royal Courts of Justice, and branched out to Finsbury Square, and an empty magistrate's court on Old Street. As other world cities have seen similar protests violently evicted by local police, the occupiers of London have clung on through a winter that has seen the nature of the camps change profoundly.

"I came here for the community," says Declan, 29. "Before this I was living in Galway, essentially trying to get together enough weed to get through the day. It's better here." He passes a glowing spliff around the other roof-dwellers. The tranquility group, with its strict policy against drugs and drunkenness, would not approve this gesture of friendship. Muriel, a french artist in her forties, is excited and a little stoned, examining the walls daubed with murals, slogans and lovingly pasted pamphlets. "If bird catcher comes, occupy the sky," she says, reading off the brickwork. "That is truly beautiful. I feel that something beautiful is happening here."

As the winter drags on, many of those who have stayed are those, like Spiral and his cat, who can't or won't go home. They are the waifs and strays and nuts and eccentrics, the wide-eyed young men with theories about how computers can calculate the perfect democracy, the straggle-haired women with bags full of paintbrushes and dirt in the creases of their cheeks. For the more media-savvy organisers of Occupy London, this has created something of a public relations dilemma.

The people who live full or part-time in the camps can now be divided into roughly three categories: those who were homeless before the occupations, those who will shortly be homeless, and those who merely look homeless. Three months of sleeping in tents, washing in the bathrooms of nearby cafes and working around-the-clock to run a kitchen feeding thousands with no running water and little electricity will transform even the most fresh-faced student into a jittering bundle of aching limbs and paranoia. Even those who haven't been living here full-time have an air of righteous exhaustion about them.

This is the part where the noble adventure of political resistance becomes a straightforward slog.

There are many for whom the unglamorous parts of maintaining an honest counter-culture do not fit into the narrative of presentable protest. Last week in New York City, activists from the original occupation in Zuccotti Park were turned away at the door of an event being held in their honour, because they looked and smelled precisely as if they had been living in tents and abandoned buildings since September. In London, at St Paul's, City workers in smart suits stop to snap pictures of the camp's battered marquees, but shy away when a man dressed entirely in pillowcases offers to take a shot with them in it. They're not going to let these people anywhere near their smartphones.

The struggle to keep a polite face on the movement can slip into censoriousness. At the late-night cabaret at Occupy Justice, the empty magistrates' court on Old Street, the burlesque dancers have been forbidden to expose their breasts. "There were some people who didn't think that was a good way of furthering the cause of the Occupy Movement," says Naomi Colvin, a long-time organiser who has become one of the unofficial spokespeople of Occupy London, regularly appearing on panels and in media coverage of the protests. The walls of the courthouse are plastered with signs instructing the heaving crowd of tramps, activists and trendy young Shoreditch hipsters not to smoke, not to write on the walls, not to leave rubbish. "This is a nice place," says one of the working group leaders. "We're nice people here."

Nice, however, has rarely trembled the walls of power.

It should be noted that no amount of scrupulous cleaning stopped the police in New York, Los Angeles, Seattle and other major cities from using the excuse of "unsanitary conditions" to evict protest camps calling for banking regulation -- it's infectious ideas, not infectious diseases, that really have the authorities worried. In London, some of the cleaner activists I meet, including those who have been involved in organising the camps from the start, quietly express the opinion that eviction might now be the best thing that could happen to the occupations. But not everyone agrees.

In the back room of the courthouse I meet Tom, 24, who describes himself as "tramp liaison". Like many members of the movement with less reliable access to showers, Tom has a lot to say about the way "sociology students in jumpers" are setting the agenda. "They talk about 'the homeless problem' at general assemblies, and I stand up and say, 'I'm homeless, are you talking about me?'," he says, sipping from a can of cheap Polish lager. "Yeah, there's definitely tension. All the camp beauraucrats will come up to you and say, 'oh, you can't roll a spliff in the uni tent', and I'm like, 'fuck off man, I'm an activist. I've been out fighting the EDL in Barking all morning'."

The main bone of contention is not drugs, but direction. Some activists are unhappy that Occupy London has chosen to work so closely with the Church on whose ground they have been camped for three months. The St Paul's occupation, which now describes itself unconfrontationally as a "guest" of the Cathedral, has without doubt had its radical bite dulled by the Church of England's grudging, eventual decision to work with the protests. Religiosity seems to ooze out of the flagstones here: ministers and police officers wander unopposed through the camp, which is festooned with signs asking "what would Jesus do?". Three months on, those signs have lost all their irony.

Others believe that movement has been taken over by external lobby groups with their own agenda, and still others are concerned that the general assemblies are choosing to focus, in Tom's words, on "the legal thing". Much of the camps' energy has indeed been directed towards fighting running battles to keep the sites open, and occupiers in the legal working groups hope to set a precedent in English case law to protect protesters' rights to free expression under Article Ten of the European Convention on Human Rights.

This explains some of the anxiety about keeping the camp clean and presentable. "We're really trying to keep the occupation fluffy," says Anna, 31. "There are some people living here who just aren't very used to being listened to." Anna, showing me around an impromptu pro-Palestine photography exhibition in the courthouse, describes the camp's internal conflicts with a generosity that is typical of the Occupy movement at its best. "It's been a massive learning curve for all of us here," she says. "Although, yes, the drinking can be a problem. I think if Occupy achieves anything at all, it'll be a whole load of people getting their voices heard for the first time."

There is a stubborn percentage of the 99 per cent who will never be able to communicate their message politely on Newsnight. Back at the Bank of Ideas, an overweight old man called Boba cannot make it up the stairs because he uses a wheelchair and the lifts are out of order. Throughout the night, the younger and sprightlier occupiers ferry the makings of sweet tea and pieces of food on scrupulously clean plates up and down the stairs to him, and are rewarded with conversation. All of this gives the lie to Orwell's axiom that "serenity is impossible to a poor man in a cold country".

On the roof, the talk turns to meditation, and to the spiritual toxicity of the banking sector. A young Romanian man called Valentin will not stop grabbing my hand and demanding my phone number. Subtle and then decidedly unsubtle hints about personal space do not put him off, and eventually Muriel invites me to sleep beside her; I observe, not for the first time, that there are far fewer young women here than there were in November. When I wake in the morning, someone has put a borrowed sleeping bag around my shoulders. There is a dawn chorus of hippies and homeless teenagers coughing up last night's tar, and the kettle is on.

There are different ways of being on the streets, and all of them are political. As the recession immiserates more and more of us, resistance will increasingly become a process of negotiating trauma, of developing economies of care that include the lost, the destitute, the down-and-out, those who cannot be "fluffy" because they have become crusted over with the debris of desperation. When these occupations are evicted, not everyone involved will be able to go home, scrub the dirt out of their hair and go back to work. Those who have lost their jobs and homes, those who left them to protest, and those who never had them in the first place attract disapprobium from their own side as well as from those determined to slander the anti-capitalist movement as filthy and unkempt. Useful activism, however, usually involves getting your hands dirty.