“Yes we can!” – “¡Sí se puede!” – is the deafening chant that closes the rallies. Except they feel less like political meetings and more like rock concerts. On Sunday, millions of Spaniards will vote in their country’s general election – not since the death of Franco has Spain faced such a dramatic political transformation.

Podemos – Spanish for “we can” – is a party less than two years old, but a combination of discontent and optimism means the party and its allies could win dozens of seats in the Spanish parliament, a political ascent lacking precedent in postwar western Europe. A combination of economic crisis, a brutal programme of cuts, and disillusionment with a political elite widely regarded as corrupt and venal spurs on its support. This election matters – not just for Spain, but for Europe too.

Travelling across Spain – and full disclosure, I’m here to support Podemos – reveals a country with a huge level of political engagement. In A Coruña, Galicia, hundreds of young people cram into a room, debating violence against women, the democratisation of the economy, and workers’ rights.

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I meet the mayor, Xulio Ferreiro, who was swept to power along with other Podemos-backed candidates in many cities in May’s local elections. Dressed in casual jeans, jumper and shirt, he is a far cry from the opulence of the city hall. It is a reminder that protesters have become rulers. In Asturias – where miners in 1934 revolted against a rightwing government before the civil war – thousands of people waving purple balloons chant “remontada”, or “comeback”, referring to Podemos’s apparent upturn in the polls. In a working-class district of Barcelona, supporters of Podemos’s allies En Comú Podem cheer Ada Colau, their new crusading mayor, who came to prominence as an anti-eviction champion.

Given what has happened to Spain, it would perhaps be more surprising if this political convulsion had not taken place. Unemployment peaked at a quarter of the workforce in 2013, and remains above 20%. The crisis was particularly ruinous for young people, nearly half of whom remain out of work, a total only eclipsed in the European Union by austerity-ravaged Greece. Many of those driven into the ranks of the unemployment were stripped of benefits, leaving them destitute.

For many of those in work, life is increasingly defined by precariousness and insecurity. According to the Financial Times, only 7% of new work contracts signed in July were for permanent jobs; before the crash, it was closer to 12%. In June, over a quarter of new fixed-term employment contracts lasted a week or less, up from just under 16% before the crash. This is the lot of middle-class and working-class Spaniards alike.

In 2014, nearly a hundred families were thrown out of their homes every day. The economic recovery has been accompanied by booming child poverty: according to the EU, one in three Spanish children now risk poverty or social exclusion. Services have been decimated too: Madrid cut 13.6% of spending on health between 2009 and 2013.

You might expect PSOE – Spain’s equivalent of the Labour party – to be the beneficiaries, but this technocratic outfit was in power when the crisis hit and began the process of cutting. PSOE shows the same signs of morbidity afflicting European social democracy: the fragmentation of its traditional base, and its acceptance of market economics and austerity at the expense of supporters.

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Election speeches here are peppered with references to the indignados, a huge movement against the entire political elite which took to the streets in the run-up to the 2011 election that evicted PSOE. The movements had two major political outcomes: the creation of Podemos at the beginning of 2014, which went on to take five seats in the European parliament just four months later; and sweeping gains for anti-austerity movements in last May’s local elections, with so-called “mayors of change” taking power in cities across the country. Podemos’s rise was meteoric: months after its foundation, some polls put the party in first place.

The first thing you notice about a Podemos rally is a rejection of the style of the old left: no red flags, no speeches peppered with socialism. As one candidate for En Marea, an ally of Podemos in Galicia, put it to me, she doesn’t answer the problems of farmers by whipping out a copy of Das Kapital. The Podemos strategy appeared to be vindicated.

But the party suffered a number of setbacks. When Syriza swept to power in Greece at the beginning of 2015, Podemos’s leader, Pablo Iglesias, forged a close alliance with Syriza’s Alexis Tsipras. EU leaders were aware that any success for Syriza would boost similar movements elsewhere, and in Spain most of all – which partly explains their determination to impose a humiliating austerity agreement. The Greek capitulation damaged Podemos.

Facebook Twitter Pinterest ‘The election campaign has transformed Podemos’s fortunes.’ Photograph: Emilio Morenatti/AP

Then there is the backlash against the burgeoning Catalan independence movement. Like David Cameron stirring anti-SNP hostility so successfully in Britain’s general election, so the Spanish government has tapped into anti-Catalan resentment, damaging the pro-referendum (though not pro-independence) Podemos.

After years of economic trauma, any sign of recovery undoubtedly benefits the incumbent government. And Podemos’s role as the new, fresh outsiders was robbed by the rise of Ciudadanos (Citizens), led by the telegenic Albert Rivera, who first came to prominence when he appeared naked in a campaign poster, cupping only his manhood.

Originating in Catalonia as a vigorously anti-independence movement, the party attracted derisory support in national opinion polls at the beginning of the year. Although portrayed as centrist equivalents of Britain’s Liberal Democrats, Ciudadanos blends free-market ideology and libertarianism on drugs and sex work, while in Catalonia it proposed banning the burqa. Some of its leading figures and candidates have suggested limiting abortion rights and removing healthcare from immigrants. Ciudadanos subsequently became the darlings of the mainstream media and surged past Podemos, apparently consigning Iglesias’s then-flagging party to fourth place.

Yet the election campaign has transformed Podemos’s fortunes. The latest polls put Podemos on 20%, four points ahead of Ciudadanos and just five points behind the ruling party, an indication of how much Spanish politics has fragmented. Though we must treat polls with scepticism, the old party system is on course to be dealt a crippling blow, even if a weakened Popular party clings on to power, possibly propped up by Ciudadanos.

Even if Podemos only wins, say, 13%, it would be a dramatic breakthrough for a party founded only last year. Let’s not get swept away: Syriza was the great hope of the left at the start of 2015. But Spain is not Greece, and Podemos shows there’s life in the movement yet. Europe’s rulers should take note.