FN leader claims 'the people have spoken', as far-right party polls an historic 25% of votes in the European elections

It was, as even their avowed opponents agreed, an historic victory. Or as French foreign minister Laurent Fabius succinctly put it, there was "one winner and a lot of losers".

From the beginning of the European election campaign weeks ago Marine Le Pen was insistent that Sunday evening would finally see the Front National emerge as "France's number one party".

Election pundits scorned her pretensions; the opinion polls confirmed them.

As the election results were predicted – and later confirmed – on Sunday evening, there were cheers followed by an enthusiastic but not particularly in-tune rendition of La Marseillaise from the party faithful gathered at the FN headquarters in the Paris suburb of Nanterre.

The far-right FN had done better than even it had probably expected or hoped, polling a historic 25% of votes in the European elections and becoming France's top party on the European stage.

As she arrived at the FN power base, supporters broke out into cheers and chanted "Marine, Marine."

"The people have spoken. Our people demand one type of politics: they want French politics by the French, for the French, with the French. They don't want to be led any more from outside, to submit to laws," a jubilant Le Pen told supporters.

"The sovereign people have proclaimed loud and clear … that they want to take back their destiny into their own hands.

"We must build another Europe, a Europe of free and sovereign nations and freely decided cooperation. Tonight is a massive rejection of the European Union.

"If Germany has become the economic heart of Europe, through the incompetence and weakness of our leaders, then France has been and will be the political heart of Europe. What is happening in France signals what will happen in all European countries; the return of the nation.

"To all those French who voted for us, I say that the battle for the greatness of France should unite us in the rediscovered love of our country."

If the result was a humiliation of the opposition centre-right UMP, which polled just over 20% of the vote, it was yet another damaging and comprehensive trouncing of the ruling Socialists, which came in third. Vote predictions said the Parti Socialiste (PS) score was 13.9% at worst and still only 16% at best.

The defeat was the second slap in the face for President François Hollande's administration in as many months after his party's disastrous showing in local elections in March, and his ministers could do little else but admit it.

Manuel Valls, the Socialist prime minister, described the election result as a "very serious moment for France and Europe", even as the FN was calling for his resignation along with the rest of the government. Valls's funereal expression showed he meant every grave word.

"The result is more than another warning; it's a shock, an earthquake," he said. He vowed, however, to push on with reforms, saying: "There is not a moment to lose."

There was no room for complacency among the opposition UMP, already riven by leadership rivalries. The party president, Jean-François Copé, tried to put a brave face on the result and deflect the blame onto the government. "It's above all a huge disappointment, but it's a reflection of the French people's immense anger and exasperation over François Hollande's politics," he said.

Copé's rival within the party, the former prime minister François Fillon, said the UMP's credibility had been seriously damaged by the result. Even Alain Juppé, another former centre-right prime minister and seen as a party peacemaker, waded in. The score he said was a severe defeat for the right and the centre. "The UMP must change. We must have a clear examination of what has happened," he said.

The rate of abstention in France was just under 57%, slightly lower than the 2009 European elections.

The initial results gave the FN 24 seats in the European parliament, the UMP 19 seats, 13 for the PS, six for the Greens and four for the Front de Gauche.

The FN's founder who is also Le Pen's father, Jean-Marie Le Pen, called for the dissolution of the Assemblée Nationale and for the prime minister Manuel Valls to resign.

A meeting called by UMP head Jean-François Copé was reportedly tense, according to a source.

On a personal level, it was a triple victory for the Le Pen clan. Marine Le Pen was predicted to have won 32.6% of votes in her constituency in north west France, her father was thought to have polled 28.9% in his south-eastern constituency and Le Pen's partner, Louis Aliot, won his seat with 23.7% of the vote in the south-west against former UMP defence minister Michèle Alliot-Marie.

At the FN's headquarters in the Rue des Suisses in the western Paris suburb of Nanterre, visitors are greeted with a statue of Joan of Arc, the party's heroine and figurehead, in full battle pose. On the internal terrace is an enormous fibre glass statue of a cockerel, another Gallic totem. French tricolor flags are everywhere.

Party officials had been optimistic, judging by the rows of champagne glasses ranged on a table in the HQ.

The FN has pledged to close France's borders to stop "the free movement of the Roma", (foreign) delinquents and "cheap foreign labour", to ditch the euro and return to the franc, to end free trade agreements with America, and "to defend, in all circumstances, our values, our identity, our traditions and our way of life".

In its election material Le Pen had urged the French to vote, insisting that shunning the polls was a vote for what it calls the UMPS, a conflation of the acronyms for two main parties, the opposition Union pour un Mouvement Populaire and the Parti Socialist.

"Today, France is at a crossroads," she wrote in her election declaration distributed to homes across the country. "Either she becomes once more a great country that is free, independent, safe, prosperous and proud of its history and read to fight for its future and that of its children. Or it disappears in a Europe-ist magma, multicultural, without influence of power, undermined by precocity and shunted wise by a savage globalisation of which the European Union is only the first step."

She concluded: "Unemployment, the loss of social benefits, injustices, the loss of our values, uncontrolled immigration are not inevitable but the result of political chooses that we can oppose, that we must oppose. France has still a future and needs you."

The FN has repeated the mantra that it has become a major force in French politics at almost every election for years, but following an unprecedented victory in last month's local election in which the far-right won control of more than a dozen town and city halls, it has become more than just wishful thinking of the past.

As Le Monde wrote after Sunday's estimations: "Marine Le Pen has won her bet: the Front National is the main winner in the European elections".

The paper added: "If the extreme right party's victory is no great surprise, the opinion polls having anticipated it for the last few weeks, the scale is surprising."

Jean-Yves Camus, a researcher at the French political think-tank IRIS, wrote in Slate.fr "The particularity of the Front National is that it cannot take part in any government or even regional coalition. It's opponents are very diverse but have one thing in common: the wish not to govern with it (the FN). It's a weak position.

"A major party is one that is able to transform its manifesto into political decisions, whereas the position in which the FN will find itself in the European parliament is of a marginalised opposition, in the same way the two FN MPs in the French parliament are very isolated."

Before the results, Slate said the only place the FN would become the "number one party in France" was on Facebook where its page had 157,000 likes compared with 84,500 for the Parti Socialiste and 82,100 for the centre-right opposition UMP party.