It's the coldest day of the year, and I've just spent seven hours being kettled in Westminster. That sounds jolly, doesn't it? It sounds a bit like I went and had a lovely cup of tea with the Queen, rather than being trapped into a freezing pen of frightened teenagers and watching baton-wielding police kidney-punching children, six months into a government that ran an election campaign on a platform of fairness. So before we go any further, let's remind ourselves precisely what kettling is, and what it's for.

Take a protest, one whose premise is uncomfortable for the administration -- say, yesterday's protest, with thousands of teenagers from all over London walking out of lessons and marching spontaneously on Westminster to voice their anger at government cuts to education funding that will prevent thousands from attending college and university. Toss in hundreds of police officers with riot shields, batons, dogs, armoured horses and meat wagons, then block the protesters into an area of open space with no toilets, food or shelter, for hours. If anyone tries to leave, shout at them and hit them with sticks. It doesn't sound like much, but it's effective.

I didn't understand quite how bad things had become in this country until I saw armoured cops being deployed against schoolchildren in the middle of Whitehall. These young people joined the protest to defend their right to learn, but in the kettle they are quickly coming to realise that their civil liberties are of less consequence to this government than they had ever imagined The term "kettle" is rather apt, given that penning already-outraged people into a small space tends to make tempers boil and give the police an excuse to turn up the heat, and it doesn't take long for that to happen. When they understand that are being prevented from marching to parliament by three lines of cops and a wall of riot vans, the kids at the front of the protest begin to moan. "It's ridiculous that they won't let us march," says Melissa, 15, who has never been in trouble before. "We can't even vote yet, we should be allowed to have our say."

The chant goes up: "What do we want? The right to protest!" At first, the cops give curt answers to the kids demanding to know why they can't get through. Then they all seem to get some sort of signal, because suddenly the polite copper in front of me is screaming in my face, shoving me hard in the back of the head, raising his baton, and the protesters around me are yelling and running back. Some of them have started to shake down a set of iron railings to get out, and the cops storm forward, pushing us right through those railings, leaving twenty of us sprawling in the rubble of road works with cracked knees. When they realised that they are trapped, the young protesters panic. The crush of bodies is suddenly painful -- my scarf is ripped away from me and I can hear my friend Clare calling for her son -- and as I watch the second line of police advance, with horses following behind them, as a surge of teenagers carry a rack of iron railings towards the riot guard and howl to be released, I realise they're not going to stop and the monkey instinct kicks in. I scramble up a set of traffic lights, just in time to see a member of the Metropolitan police grab a young protester by the neck and hurl him back into the crowd.

Behind me, some kids have started to smash up a conveniently empty old police van that's been abandoned in the middle of the road. "Let us out!" they chant. "Let us out!" A 13-year old girl starts to hyperventilate, tears squeezing in raw trails over her frightened face, unable to tear her face away from the fight -- I put a hand on her back and hurry her away from the police line. Her name is Alice and she is from a private school. "Just because I won't be affected by the EMA cuts doesn't mean I don't care about the government lying," she says, "but I want to go home now. I have to find my friend."

As darkness falls and we realise we're not going anywhere, the protesters start to light fires to keep warm. First, they burn their placards, the words "Rich parents for all!" going up in flames, with a speed and efficiency gleaned from recent CV-boosting outdoor camping activities. Then, as the temperature drops below freezing, they start looking for anything else to burn, notebooks and snack wrappers -- although one young man in an anarchist scarf steps in to stop me tossing an awful historical novel onto the pyre. "You can't burn books," he says, "we're not Nazis."

As I look around at this burned-out children's crusade, I start to wonder where the hell the student activists are. Whatever the news says, this is emphatically not a rabble led by a gang of determined troublemakers out to smash things for fun. In fact, we could do with a few more seasoned radicals here, because they tend to know what to do at demonstrations when things get out of hand. I find myself disappointed in the principled anarchists and student activists I know, who aren't here because they've decided that the best way to make their presence felt is by occupying their own lecture halls. I realise that these school pupils are the only ones who really understand what's going on: even people my age, the students and graduates who got in just before the fee hike, are still clinging to the last scraps of that dream of a better future, still a little bit afraid to make a fuss. These teenagers, on the other hand, know that it's all nonsense. They sat their school exams during the worst recession in living memory, and they aren't taken by the promise of jobs, of education, of full lives and safe places to live. They understand that those things are now reserved for the rich, and the white heat of their rage is a comfort even behind the police lines in this sub-zero chill.

Smaller children and a pregnant woman huddle closer to the fires. Everyone is stiff and hungry, and our phones are beginning to lose signal: the scene is Dante-esque, billows of smoke and firelight making it unclear where the noises of crying and chanting and the whine of helicopters are coming from.

This is the most important part of a kettle, when it's gone on for too long and you're cold and frightened and just want to go home. Trap people in the open with no water or toilets or space to sit down and it takes a shockingly short time to reduce ordinary kids to a state of primitive physical need. This is savage enough when it's done on a warm summer day to people who thought to bring blankets, food and first aid. It's unspeakably cruel when it's done on the coldest night of the year, in sub-zero temperatures, to minors, some of whom don't even have a jumper on.

Some of them have fainted and need medical attention, some need the loo. They won't let us out. That's the point of a kettle. They want to make you uncomfortable and then desperate, putting your route back to warmth and safety in the gift of the agents of the state. They decide when you can get back to civilisation. They decide when the old people can get warm, when the diabetics can get their insulin, when the kid having a panic attack can go home to her mum. It's a way of making you feel small and scared and helpless, a way for the state's agents to make you feel that you are nothing without them, making you forget that a state is supposed to survive by mandate of the people, and not the other way around.

Strangers draw together around the makeshift campfires in this strange new warzone right at the heart of London. A schoolgirl tosses her homework diary to feed the dying flames. "I don't even know you, but I love you," says another girl, and they hug each other for warmth. "Hands up who's getting a bollocking from their parents right now?" says a kid in a hoodie, and we all giggle.

He's got a point. This morning, the parents and teachers of Britain woke up angry, in the sure and certain knowledge that the administration they barely elected is quite prepared to hurt their children if they don't do as they are told.

It's not looking good for this government. This spontaneous, leaderless demonstration, this children's crusade, was only the second riot in two weeks, and now that the mums and dads of Britain are involved, the coalition may quickly begin to lose the argument on why slashing the state down to its most profitable parts and abandoning children, young people, the disabled and the unemployed to the cruel wheel of the market is absolutely necessary.

Let the government worry about the mums and dads, though -- I'm worried about the kids.

I'm worried about the young people I saw yesterday, sticking it out in the cold, looking after one another, brave and resolute. I'm worried about those school pupils who threw themselves in front of the police van to protect it from damage, the children who tried to stop other children from turning a peaceful protest into an angry mob -- and succeeded. I'm worried that today, those children feel like they've done something wrong, when they are, in fact, the only people in the country so far who've had the guts to stand up for what's right.

The point of a police kettle is to make you feel small and scared, to strike at the childish part of every person that's frightened of getting in trouble. You and I know, however, that we're already in trouble. All we get to decide is what kind of trouble we want to be in. Yesterday, the children of Britain made their decision, and we should be bloody proud of them today.

Read Laurie Penny's account of the original student protests, where dozens of students attacked the Conservative party's HQ here. You can follow her on Twitter here.