In Trafalgar Square, the worst November snowstorms in decades are pummelling thousands of teenage protesters more effectively than any police kettle. The cops are there anyway, of course, clotting every exit from the square like rotten yellow scabs, sealing off the social dissidence from the more compliant tissue of the body politic. Right now Her Majesty's Finest are being reasonable, but earlier in the day, when these young protestors abandoned the planned route for their march after a tip-off that police planned to detain them again in the freezing sleet, it was a different matter altogether.

Videos are already emerging of police officers repeatedly punching children in the face, as one girl describes how her friend narrowly escaped death. "Some people had already gone through the kettlle, and Sarah screamed for people to come through. A policeman shoved her in the chest, and she fell into the road in front of a truck, which stopped about two feet away from her." Other witnesses later confirm this account.

I am leaning on a set of railings because my feet, frozen through from a seven-mile spontaneous rampage round central London, will no longer support me. Kids are still piling into the square from all directions, exhausted but undefeated, having walked out of school and university occupations across the city and come to join the shakedown. Now they are gathering in one corner of the square, screaming and hugging each other despite the howling wind. In the gusts of snow and debris, over the drone of police helicopters, the indefatigable samba band begins to play and a ragged cheer goes up. Britain's children's crusade has not been cowed by police brutality: they are dancing in the snow. Some of them quite obscenely.

The march from which they are returning has been a wild, rampant charge, two thousand protesters careering up Piccadilly, past the Ritz and the Trocadero, letting off smokebombs and chanting "no ifs, no buts, no education cuts!" under the corporate-sponsored Christmas lights of Oxford Street. To the bewildered tourists and salarymen snapping pictures from shopfronts this probably looks like chaos - but the chaos is terribly organised.

"I have no idea where we're going," says Melissa, 22. "Nobody does, and that's why it works." "If we don't know where we're going the police don't either," says her friend, "and that means they can't kettle us or catch us. It's perfect."

"These strategies for avoiding police brutality have been around since 2001," says the writer Shiv Malik, who is also at the protest, "but nobody actually sat down and thought about how to put them into action before. This is very clever - these kids learn fast," he pants as he tries to keep up with the mach. "Well, they are students, I suppose."

Before long, it's a cat-and-mouse game as police try to head off the march at various street exits; the young protesters simply veer off in the other direction, laughing and jeering. Sirens scream in the distance, but the police can't keep up with the pace of the march. It could be a Benny Hill sketch if it weren't for the bitter cold and the police meat wagons gathering on street corners.

As we go past Topshop, the students begin to shout about Topshop owner Sir Philip Green, one of many billionaires to benefit from this administration's generosity towards big business. "Philip Green - tax avoider!" they yell. Avoider, not evader. With a start, I realise that these young people have taken time out from smashing windows to share information on how to avoid being sued for libel.

Britain's new youth movement has evolved. The white-hot energy that exploded at Millbank three weeks ago has cooled into a hard-edged organising tool, making links with Trade Unions and anti-cuts groups up and down the country. What started as a riot has become a movement. At UCL, one of the movement's strategic hubs, serious-faced teenagers take detailed notes and man the phones to liaise with the media whilst others are already at their laptops, getting the word out via Twitter and Facebook about what's happening on the streets. These young people have been underestimated - by their parents, by their teachers and lecturers, and by successive neoliberal administrations -and that underestimation may yet shake this government to its core.

Evenings in the occupied lecture halls across the country are a jumble of joyful anti-establishment clichés, all twee improvised sing-songery and communal cooking and belting out the Internationale whilst someone presses more beer into your hands - but these are not the hedonists of 1968, and there is a strict divide between business and pleasure. There's a cleaning rota, booze is rationed to prevent rowdiness, and nobody is allowed to drink whilst decision-making meetings are taking place.

The interminable meetings are based on a complicated consensus system involving wiggly hand-signals. At times it all descends into Pythonesque farce as the students discuss the exact legal status of chalking messages on the pavements - but there's a point to it all. "The process is meant to prevent leaders emerging," one student informs me. "It's important to make sure everyone's voice is equally heard."

These young people are sick of leaders, even leaders our own age. They won't be told what to do, but that sentiment is more of a honed manifesto than a collective teenage door-slamming strop. When the meeting is over and consensus reached, the collective slams back into action, planning an escalation in the protests leading up to the crucial vote on tuition fees later this month.

These protesters have a honed protestant work ethic, a coherent ideological framework, stunning technological facility and absolutely nothing to lose. No wonder the administration is getting worried. The students at UCL are now desperately mustering plans to defend their organising space, which may soon be forcibly evicted by police who are no longer quite the friendly bobbies from children's telly. In fact, the police seem more determined to punish these protesters extra-judicially for their defiance the clearer it becomes how little actual crime they are committing.

As night falls on the makeshift rally in Trafalgar square and I begin to feel faint from the chill, someone directs me past the stamping crowd on Nelson's column to the tea-stand. The students from SOAS have brought hot tea and homemade cookies and are selling them for pennies as a "gesture of solidarity." "It's a new world order!" says a girl behind me in the queue.

Sitting on a fountain in Trafalgar square, slurping a nice hot cup of tea in the freezing rain and snow, watching the children's crusade brave the elements and police lines to chant for the downfall of a government it sees as corrupt and illegitimate, I have never felt prouder of my generation.