Last Wednesday morning Alice, aged 16, set off from her school in north London with fellow sixth-formers on her first demonstration. The night before, she and her friends had prepared their slogans and were raring to go. The national student protest against tuition fees had fused a dissident teenage cocktail of anger, anxiety and frustrated ambition into a determination to make her voice heard on the street.

Alice's mother, Anne, who does not want her daughter or her school to be identified in case it jeopardises her career, says she was intrigued to watch her previously apathetic daughter become politically aware. "Alice is a very conscientious student who never misses a day of school," she said. "Until a year ago she showed no interest in politics."

The sight of Alice with her "9K No Way" placard stirred mixed memories of her own radical youth – Greenpeace sit-ins and Free Nelson Mandela marches – and she watched her daughter and friends head off to Trafalgar Square "like babes in the wood", expecting them home by teatime.

What happened next to Alice and her friends and to thousands of London school kids – all "Harry Potter children" – in the eight or so hours between arriving in Whitehall full of hope and excitement and straggling back through the dark, cold, angry and disillusioned, to the comfort of home and family, is one kind of snapshot of coalition Britain. From a wider perspective, the run-up to the Kids' Kettle was also a classic moment of anti-government fury in the tradition of English protest, an odd mixture of street action and street party.

This was certainly a strange rebellion. Many of the demonstrators were in ties and blazers and ill-disguised items of school uniform. Some of them came with their school bags and homework. A few were equipped with snack lunches and bottled water thoughtfully provided by their parents, who had dropped their children, by car, at the start of the demo. Their banners referenced Hogwarts and Voldemort. The whole event was middle-class, self-interested and respectable. Much of the preparatory organisation had occurred through Twitter and on Facebook. At first the protest was more a product of social networking than socialism.

The demo was the creature of the mass media in many other ways, too. Until the ground-breaking general election television debates, many unenfranchised schoolkids showed virtually no interest in politics. But those debates changed everything. The surge of support for Nick Clegg among voters was driven, bottom-up, by the enthusiasm of a teenage audience.

Amy Dunne, now part of the coalition of resistance (coalitionofresistance.com), describes herself as "an idealist and a socialist", though she thinks "the socialist revolution probably won't happen in my lifetime". After the TV debates, Amy says, "my mum voted Lib Dem". If she had been eligible Amy "would have voted Lib Dem". When Clegg reneged on his election manifesto pledge on tuition fees, many sixth-formers felt that Clegg had let them down. "We felt betrayed," says Isabelle from Highgate Wood school. "Yes, I was angry for myself."

To a greater or lesser extent, this was the mood of the majority of the estimated 10,000 who assembled for the march on parliament at midday on Wednesday. Everyone, including many of the kids, seems to agree that the demonstration was, in the words of one, Miriam Skrentny from Camden high school, "not about revolution".

These were Blair's children and they have a strong sense of entitlement. They expect to be listened to. Miriam adds: "I wasn't really sure what I felt about the coalition's policies, but I wanted the government to pay attention to my concerns." Her baby-boomer parents will have heard this phrase often enough, but will have never seen it transferred to the street. Unlike the baby-boomers, for whom the police were "the pigs" or "the fuzz", this new generation of protesters had a benign, slightly naive view of the police. Miriam says that before the demo began she saw the police as "a helping hand", not an instrument of state control. All this was about to change.

As the demonstrators assembled by Nelson's Column, the placards were unanimous – anti-tuition fees, anti-Clegg, mixed in with protests against the coalition's cuts. Tuition fees were the core for the protest. Behind the fears for their future as students and adults, there were many levels of anxiety about the world bequeathed to them by their parents who had, in the words of one mother, "enjoyed peace, prosperity and free schooling".

The youngsters' rage is that, despite these advantages, their parents' generation had handed on a global meltdown: global warming, global debt and global insecurity. Several of the university students who provided a more grown-up presence at the protest were quite explicit in their concerns.

Elizabeth Squires, who travelled from Cambridge, said: "I was protesting not so much for me, because although I'm already in debt at least I've nearly finished my degree. I'm protesting for the next generation, who will be paying for their education for decades."

The last time that students – the parents of these demonstrators – marched in any numbers, during the 1970s and 1980s, they were motivated not by the cost of tuition but by a desire to change the world, to end apartheid, to ban the bomb or make peace in Northern Ireland. Again, behind the youthful idealism of the 1970s there was a rich textual hinterland: the works of Marx and Marcuse, Trotsky, Fanon and Mao.

These young Facebook radicals have strong feelings and well-argued ideas, but their stance is empirical, not theoretical. It relates to a set of anxieties about the future. They are also savvy about getting their message across. One schoolchild, Zoe Williams, who attempted to moderate an outbreak of violence, was heard to say: "We are going to be portrayed badly in the media."

As well as being self-conscious, even fashionable, Wednesday's march was optimistic and broadly peaceful at the outset. The few anarchists and professional agitators in balaclavas, who would be responsible for the televised attack on a police van, were a heavily outnumbered minority. As Alice and the novice demonstrators set off down Whitehall and approached Parliament Square, they encountered a police barricade and turned to go home. Except they couldn't. They were "in the kettle".

It took a while for the kids to realise what was happening. Miriam, whose father had warned her about "kettling", attempted to speak to the police, but got nowhere. After the Millbank debacle, the face of the Met was ugly, provocative and hostile.

"What was scariest," says Ailsa, 16, "was that people were going crazy at being trapped and also at the injustice of the whole thing. Some of the marchers seemed drugged up. They were dancing. There was a rowdy corner where people were playing music and having a kind of party." In some newspapers, this was reported as students dancing the hokey-cokey. This did not last long. The protesters were cold, hungry, thirsty – and there were no toilets. There was not much they could do about their hunger but share out chewing gum. To keep warm, some of the crowd made fires from schoolbooks and street refuse. In the absence of toilets, the kids had to use the gutters in the street, or improvised shelters made from discarded banners. Another school student, Jack Saville, described his experience: "Resentment at the government education cuts was replaced by resentment at the police." The chants of "No ifs, no buts, no education cuts" morphed into more desperate cries of "Let us go!"

For everyone in the kettle it was a radicalising experience. The protesters were acutely conscious of being denied their right to march. "We were being treated as criminals simply for turning up," said Saville. Volunteer trainee lawyers passed through the crowd with leaflets about the students' rights. The kids, meanwhile, texted frantically. One mother rang the Metropolitan police helpline, where "a very sympathetic policewoman" did what she could to offer reassurance and guidance.

Other parents advised their kids on how to keep out of trouble. On the ground, the mood was hardening. They could see that the police had used "the kettle" as a deterrent. "They were planning to stop us," says Ailsa. "They kettled us to discourage us from future demos. Now we will have to go – to show that we're not cowed."

Scotland Yard also later came under pressure after video footage emerged of police officers on horseback charging protesters near Trafalgar Square.

Parents who had been philosophical during the long, cold afternoon became more fearful as darkness fell. "When will our children come home?" asked Ted, a public sector worker from Camden. "Yes, I was really worried once night fell. My daughter was not released until 7.30pm and got home after 8pm. I remember how the police killed that news vendor Ian Tomlinson. Next time, maybe, children will get hurt."

Alice and her friends from Crouch End came back at 9pm with a copy of Socialist Worker and a souvenir placard: "Tory Scum, Here We Come". Alice's mother was pleased to see the newspaper. "It's been a while since I've read Socialist Worker," she said, noting with interest that her daughter was now wearing combat stripes on her cheeks.

There are more demonstrations planned. The students seem now more determined to protest than ever. Miriam Skrentny believes that the real losers are the Lib Dems. "Nick Clegg is finished," she says. "No one will ever vote for him again now."