The symbolism of Vox’s election campaign launch in Madrid on Thursday was not particularly hard to fathom. In the central square named after Christopher Columbus, near a statue of Blas de Lazo, the battle-scarred, one-legged Spanish admiral who vanquished the British fleet off Colombia 278 years ago, the far-right party’s leader issued a familiar call to arms.

Vox weren’t after anything as prosaic as votes, Santiago Abascal told the crowd. What he had in mind was a political crusade to fly “the flag of Spain and of liberty” across the country and to take the fight to the “illegitimate” socialist government, an administration propped up by parties he termed “separatists, populists and friends of terrorists”.

His followers responded with cries of “Prime minister! Prime minister!”

Although such ambitions remain staggeringly lofty, Vox is nonetheless on course for a remarkable breakthrough into the political mainstream. If the polls are to be believed, the party will take around 10% of the vote on 28 April, making if the first avowedly far-right grouping to win more than a single seat in the national parliament since Spain returned to democracy after the death of General Francisco Franco in 1975.

Vox, which was founded six years ago by disgruntled members of the conservative People’s party (PP), used to be seen as a tiny fringe group. But all that changed in December last year when Vox wildly exceeded expectations to take 12 seats in the Andalucían regional election.

The Andalucían vote had two dramatic and enduring consequences: not only did it see the socialist PSOE turfed out of office in its traditional stronghold, it also confirmed both the advent of Vox and its growing influence on other rightwing parties.

The party quickly underlined its king-making power by backing a coalition government of the PP and the centre-right Citizens party in Andaluciá. Vox initially made it support contingent on the expulsion of 52,000 “illegal immigrants” and the repeal of laws on domestic violence and gender equality, but eventually backed down on these demands.

The PSOE, led by Spain’s prime minister, Pedro Sánchez, is on course to win the most votes at the end of the month but is likely to fall well short of a majority. Warning of the threat of a similar “triple-right” pact that could see the PP, Citizens and Vox form a national government, the socialists are aiming for a massive mobilisation of their base.

They are also hoping that competition between the three rightwing parties will split the vote, seriously damaging the prospects of the PP, which until a few years ago was the single broad church in which all of the Spanish right worshipped.

Supporters of Vox, the Spanish far-right party, wave Spanish flags. Photograph: Álvaro Barrientos/AP

The rise of Vox, fuelled mainly by the Catalan independence crisis but also by culture wars over feminism, political correctness and recentralisation, has panicked the PP and Citizens, sending both parties running to the right.

Sánchez has pointed out that the Spanish far right did not die with Franco: the Fuerza Nueva coalition of Blas Piñar won a single seat in congress in 1979, only to lose it three years later. “There’s nothing in the least new about this – the far-right has always existed in Spain,” he told the Guardian recently. “Yes, it’s worrying, but it’s not the biggest worry. Why? Because they’ll never win an election. What troubles me is the way they’re radicalising and swelling the political discourse of the other two conservative parties.”

José Pablo Ferrándiz, the chief researcher for the polling firm Metroscopia, said that with two weeks to go until polling day the only certainties seemed to be that the PSOE would win the most votes and that Vox would secure a significant victory.

“Vox may finish fifth in parliament, close to Unidos Podemos, but they’ll go from no seats to up to around 30,” he said. “That is a complete success.”

Although 40% of voters are still undecided, Ferrándiz was wary of suggestions there was a large pocket of shy Vox voters. “People wonder whether there might be a hidden Vox vote, but people who are going to vote for Vox are declaring that intention quite loudly and without any embarrassment,” he said. “I think their electoral ceiling is around 10-12% right now.”

Antonio Barroso, an analyst at the political risk advisory firm Teneo, said: “Anything beyond zero is a huge victory for them” but Vox, like other parties, ran the risk of over-inflating expectations. He recalled predictions that Unidos Podemos would leapfrog the PSOE into second place in the June 2016 general election, which never materialised. “It may perfectly well be the case that there is more support than the polls are showing but Podemos also had huge rallies – and look what happened.”

Barroso said Vox was waging a “classic radical-right populist campaign” similar to those seen in Italy and the US. The aim was to bypass the mainstream media, connect directly with voters and avoid contact with rivals so as to avoid talking about a “very thin” policy platform.

“They’re very active on social media and they put out things that are very far to the right of the political spectrum,” he said. “That triggers a conversation and a reaction by the left and others and that puts the focus on Vox, and they fine-tune the idea and say: ‘No, what we meant was …’ That creates a huge uproar that then puts the focus on them and they get coverage.”

Regardless of whether Vox once again manages to exceed expectations and confound pollsters, the party’s disruptive effect has so far proved a triumph in itself. “Given that they had zero seats in the past, they’ve already won to a certain extent just by being one of the main issues of the campaign,” Barroso said.