Front National wins European parliament elections in France.

Marine Le Pen's Front National party came first in three exit polls with more than 25% of the vote. Photograph: Remy De La Mauviniere/AP

France's nationalist extreme right turned European politics upside down on Sunday, trouncing the governing Socialists and the mainstream conservatives in the European parliamentary elections which across the continent returned an unprecedented number of MEPs hostile to, or sceptical about, the European Union in a huge vote of no confidence in Europe's political elite.

According to exit polls, the Front National of Marine Le Pen came first in France with more than 25% of the vote. The nationalist anti-immigrant Danish People's party won by a similar margin in Denmark. In Austria, the far right Freedom Party took one fifth of the vote, according to projections, while on the hard left, Alexis Tsipras led Greece's Syriza movement to a watershed victory over the country's two governing and traditional ruling parties, New Democracy conservatives and the Pasok social democrats.

The voting across four days in 28 countries, according to exit polls late on Sunday, delivered a string of sensational outcomes, with radical and nationalist anti-EU forces scoring major victories both on the far right and the hard left.

In Britain, the Nigel Farage-led insurrection against Westminster was also tipped to unsettle the polticial mainstream by coming first or second in the election. The Tories, the biggest UK caucus in the parliament for 20 years, faced the prospect of being pushed into third place.

In Germany, the most powerful EU state, Chancellor Angela Merkel's Christian Democrats scored an expected easy victory, but Germany also returned its first eurosceptics in the form of the Alternative for Germany as well as its first neo-Nazi MEP from the Hitler apologists of the National Democratic Party of Germany, according to German TV projections.

And Merkel's Christian Democrats dropped several points while the SPD (social democrats) made significant gains, narrowing the gap between the two big parties to around 8 percentage points.

The election mattered more than ever before because the Strasbourg-based parliament has gained greater powers, meaning it will have a strong say in most EU legislation over the next five years and will also shape the outcome of the battle for the most powerful post in Brussels, the new head of the EU executive or European commission. However, its mandate to exercise those powers was dented by the low turnout, at around 45%, raising renewed questions about the parliament's legitimacy.

Posters announce France's Front National as the leading political party in the country are hung at their party's HQ. Photograph: Christian Hartmann/REUTERS

If the Front National score is confirmed, it will be the first time that the anti-immigrant, anti-EU party has won a national election and would give the party 23-25 of France's 74 seats in the European Parliament.

Le Pen immediately called for the dissolution of the French national assembly after the exit polls showed her anti-immigrant, Eurosceptic party winning . "What else can the president do after such a rejection?" Le Pen told reporters at Front National headquarters when asked if Hollande should dissolve the national parliament. "It is unacceptable that the assembly should be so unrepresentative of the French people."

From the beginning of the European election campaign Le Pen was insistent that Sunday evening would finally see the Front National emerge as "France's No 1 party".

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

As the first exit polls were announced at 8pm on Sunday, cheers and a rendition of La Marseillaise broke out among the party faithful gathered at the Front National headquarters in the Paris suburb of Nanterre, appeared to prove Le Pen right.

The first estimations suggested the far-right party had done even better than expected, polling an historic 25% of votes in the European elections and becoming France's No1 party on the European stage.

It was the second slap in the face for Hollande's administration in as many months after a disastrous showing in local elections in March.

Exit polls suggested Greece's anti-austerity leftist party Syriza had come first, but the election also delivered a strong showing for neo-Nazi group Golden Dawn. With up to 10% of the vote Golden Dawn looks set to elect at least two out of Greece's 21 eurodeputies, despite an ongoing criminal investigation and the fact that several of its leading members are in pre-trial detention.

Syriza was ahead by about 3 percentage points over the leading government party, the conservative New Democracy, polls jointly carried out by six leading opinion companies showed.

Syriza's parliamentary spokesman Panagiotis Lafazanis said that if confirmed, the EU vote constituted a game-changer in Greece.

"The (EU vote) result alters Greece's political scene," Lafazanis told Mega television.

Victory for Syriza would appear to reflect popular frustration with the harsh spending cuts the government has adopted in recent years to meet the terms of its economic rescue programme.

The surge in support for the far-left raises doubts about how much longer the centre-right government can last with a parliamentary majority of just two seats, although government spokesman Simos Kedikoglou said there was no question that the government would not finish its four-year term.

"It's easy for people to cast a protest vote in European elections," he told Greek television. "The political scenario of a government collapse, which Syriza was trying to paint, has not been borne out by the facts."