The arrival of the table, a battered piece of Formica bashed on top of four rough, oversized legs, raised a cry of joy. Never mind that anyone on a normal chair would barely be able to see over the top – here was another small triumph of the new Spanish revolution, the gathering of angry Spaniards of all colours, ages and persuasions that is sweeping across the country and beyond its borders.

The table that arrived in Madrid's Puerta del Sol square was part of the swirl of creative chaos, naive enthusiasm and pent-up frustration that has transformed it into a makeshift camp for thousand of protesters who call themselves los indignados, the indignant ones.

Tents and mattresses, armchairs and sofas, a canteen, portable toilets and solar panels have sprung up in a remarkable display of organisational prowess. And the mass of people jostling around, each pursuing their own dream or demand, or just watching others doing the same, seemed more like something transported from the Arab spring in north Africa than from Europe.

As the protests continued to swell on Friday, with 60,000 people defying authorities to obey the campaign's "Take over the square!" slogan in dozens of Spanish cities, and with copycat demonstrations across Europe, the question was whether this was the new May 1968 – a youth-led popular revolt against an establishment deemed to have failed an entire generation.

Esther Gutiérrez, an elfin 26-year-old, wandered through the crowd with a battered shopping cart full of fruit. "We've got so much food we don't know what to do with it. People just bring it to us for free and it's wonderful stuff," she said. "We want real democracy. Not just freedom for bankers. You're not from the Spanish press, are you? We don't speak to them."

Cynical and ingenuous by turns, the Madrid protesters and those who refused to budge from the city squares have torn up the rule book of Spanish public politics. The heavyweights of old – political parties, trade unions and media commentators – are not wanted here.

"I was sacked when the Madrid regional government closed down a women's centre last year when it imposed cuts," explained Beatriz García as she bashed a small frying pan with a wooden spoon. "The unions didn't even bother to turn up."

The political parties were worse still, she said. "There is no renovation. There is nothing new or different, just two parties who take it in turn to govern because our electoral laws favour them."

Just a week ago the Spanish had seemed stoical about one of the most depressing eras in recent economic history. Despite unemployment hitting 21% – rising to 41% for the young – widespread spending cuts and a socialist government bound to obey the diktats of Germany's chancellor, Angela Merkel, and the financial markets, they had refused to show their pain. Marches, sit-ins or riots were for the French – or British students. The real drama, anyway, was in north Africa. Spaniards stayed at home.

All that changed as demonstrations organised via Facebook and Twitter became static protests in city squares, mushrooming into something that caught politicians, unions and the media by surprise. While journalists were following the dull routine of campaigning for Sunday's municipal and regional elections, the steam was beginning to escape from a pressure cooker of discontent.

Many Spaniards had told pollsters they were tired of the same well-known political faces – especially those who were due to be re-elected despite being mired in corruption scandals. Politicians have rarely been held in such disregard, with the prime minister, José Luis Rodríguez Zapatero, and opposition leader, Mariano Rajoy, of the conservative People's party, rating lowest. Rajoy seems set to take over after a general election next March.

When police evicted the Madrid demonstrators on Tuesday morning, they came back in even greater numbers later that day. By Friday night authorities had lost the battle to impose rules banning public politics on the day before elections. Police could only look on. "Join us, police officers!" the demonstrators shouted.

By the early hours of Friday, it was already elbow-room only in the Puerta del Sol – the square which prides itself on being Spain's "kilometre zero", the spot from which all other distances are measured.

On the statue of King Carlos III, somebody had pinned a sign that read: "We are anti-idiots, not anti-politicians." Other placards read: "We aren't against the system, we want to change it", "Democracy, a daily fight", and "Take your money out of the bank!"

"We've brought tents, food and even Trivial Pursuit to keep us entertained," said Pablo Cantó, a 23-year-old journalism student. Like many younger protesters, and the movement as a whole, he had trouble expressing exactly why he was here. "We want change," he said. "Things just can't carry on as they are."

The heavy clouds of cannabis smoke suggested others had brought their own form of entertainment.

"I've been protesting for decades," said 60-year-old schoolteacher Rosa Marín. "I'm glad to see so many young people here. The questions is this: Is this another May 1968, or are they just here for the party?"

A gang of drunken skinheads, mindlessly chanting football terrace slogans, were there for the latter.

But a neat, disciplined circle of people intently debating social reform showed many were here in earnest. They took turns to stand up and make their proposals, the audience listening and using the sign language applause of the deaf – by shaking their hands above their heads – to show approval without drowning the speakers out.

The proposals, due to make their way through a laborious process of committees, working parties and general assemblies, varied from calls for less spending on the military to helping businesses. "Because it is not just money for the owners. They are the ones who give people like us jobs," said one young man wearing combat-print shorts.

For some younger protesters, it was a political baptism. "I don't know what will come out of this, but it is enough just to show everyone how upset we are," explained Javier de Coca by phone from the protest camp in Barcelona's Plaza de Catalunya, where there was a surprising absence of the nationalist or separatist symbols of protest movements in recent years.

"It's as if they've realised they have more serious problems to deal with," said one protester. One of those problems is youth unemployment.

On a wall beside the tarpaulin-covered command centre in what some were calling Madrid's "Republic of Sol" – home to a press office, an infirmary and a legal centre – a list of needs had been pinned up. Toilet paper and food were scratched off the list. Bookshelves, wood, rubber gloves and bottles of cooking gas were on it. Volunteers were needed for a crèche.

"We process the proposals and try to turn them into something that makes legal sense," explained a volunteer at the legal centre.

However, the open assemblies are painfully slow. Some last for hours, as everybody is given their turn to speak. After almost a week of protests, the demonstrators have failed to come up with a coherent set of demands.

Electoral reform to end the two-party system and action to punish corrupt politicians and limit their privileges were the main areas of agreement.

So is the Arab spring spreading to southern Europe? "You can't really compare us to people who were risking their lives by protesting," said 23-year-old computer engineer Jaime Viyuela. "But yes, you can say that we are inspired by the courage of the Arab spring."