Depending on the complicated manoeuvring to form electoral blocs following the elections, the Greens could slide from the fourth largest caucus to the sixth.

With Nigel Farage's UK Independence party (Ukip) tipped to win in Britain, much will hinge on the affiliation of Beppe Grillo's Five Star movement in Italy, which is tipped to come second in the Italian vote with 19 seats. Should Grillo opt to make common cause with Farage, the Ukip-led Europe for Freedom and Democracy group could hold as many as 66 seats, putting it neck-and-neck with the liberals for third largest caucus behind the mainstream centre-right and centre-left blocs.

Despite suggestions that the Greens are making gains in Britain, the outlook in their core constituencies of Germany and France is dismal. The Greens slumped in Germany's elections last year, underwent a generational leadership change and are still struggling to clarify their message.

"The result was very chastening," said Cem Oezdemir, a leading German Green.

The final polling conducted across the EU by Votewatch Europe has the Greens falling to around 44 seats from 58 in the current parliament. Germany and France supplied about half the Green MEPs in the current parliament, each returning 14. The number of German Green MEPs is predicted to fall to 11, and the French to collapse to five.

Electionista's aggregate poll of polls has the Greens falling even further, to 41 seats in the 751-seat chamber.

The draconian spending cuts and austerity wrought by the eurozone crisis over the past four years have boosted support for the far left, according to the polls. Under the umbrella of European United Left, far left parties are predicted to win between 50 to 53 seats, up from 35 in the current parliament.

In the Netherlands, the far left Socialist party is running neck-and-neck with the governing Labour party in the polls. Die Linke, made up of former east German communists and disaffected social democrats, is now the main opposition party in Germany. Alexis Tsipras, the head of the Syriza movement and the annointed leader of Europe's new left, is expected to win the election in Greece.

Given the extreme fragmentation of the parliament – initially there could be as many as 150 different national parties and independents represented, compared with 76 in the current parliament – power will hinge on the wheeling and dealing that follows the vote.

"Compared to the outgoing parliament, the new parliament would be more polarised, with more MEPs on the radical left and on the right of the [Christian democrat] EPP," Votewatch Europe said.