More EU citizens have voted in European parliament elections than at any time in the past quarter century, the assembly has said, estimating overall turnout in the EU27 member states at 51% compared to 42.6% in 2014.

Voters turned out in significantly larger numbers than in the previous poll in almost all member states, including Germany, Poland, Spain, Sweden and France, where turnout was predicted to be more than 50% – also the highest since 1994.

Turnout in Hungary was on course to surge by more than half, with hardline prime minister Viktor Orbán, saying the issue of migration would “reorganise the EU’s political spectrum”.

More than twice as many Polish voters turned out as in the previous 2014 vote and turnout in Denmark hit a record 63% as Brussels hailed the end of a 40-year trend of declining turnout perceived as undermining the legitimacy of EU lawmaking.

The increased voter enthusiasm was set to benefit both pro and anti-EU parties around the bloc as voters in 21 member states went to the polls on the fourth and final day of elections described by France’s president, Emmanuel Macron, as decisive at “the most perilous moment for Europe since the second world war”.

Italy’s anti-migrant interior minister, Matteo Salvini, who is trying to forge an alliance between his far-right League, France’s National Rally, Germany’s Alternative für Deutschland and other populist parties, said he felt a “change in the air” and that a win for the League would “change everything in Europe”.

Rightwing populists were on course to finish a comfortable first in two of the EU’s big four member states – Italy and Britain, which was supposed to have left the bloc by now – and edge a narrower victory in a third, France, upsetting Macron’s pro-European drive.

But polls in some countries suggested the traffic would be far form one way. In Spain, where turnout surged to 49% from 34% in the previous elections, the staunchly pro-European caretaker socialist prime minister, Pedro Sánchez, was headed for victory.

Spaniards were voting in a “Super-Sunday” of European, regional and municipal elections, less than a month after the country’s third general election in under four years. “Today is a very important day,” tweeted Sánchez. “Today we decide the future of Europe and Spain over the coming years.”

At 41%, turnout was also up in the Netherlands, where the Dutch Labour party – all but written off – was on course to finish first and pro-EU parties scored 70% of the national vote, sharply up on 2014.

Germany’s centre-right candidate for the helm of the European commission, Manfred Weber, said he hopes most would back a stable Europe. “I don’t want to see a right-populist Europe that wants to destroy the idea of togetherness,” he said.

Italians went to the polls after a divisive campaign that left many feeling confused and worried as key parties failed to offer up clear and positive policies for Europe.

“A European election campaign has never felt like this before,” said Gualtieri Pinci after casting his vote at a polling station in central Rome. “Right up until the moment I entered the booth, I didn’t know who to vote for. No party has a clear vision, just lots of vague declarations.”

Maria Carolina Cirillo said Salvini had “exploited bad feeling, but Europe made it easy for him to do so. We need to be more united.”

Another voter, Cinzia Canti, added: “Usually us Italians don’t expect much from voting, but the EU elections are important. It’s important that we have peace, solidarity and acceptance of others – I’m afraid of our current government, which is hostile towards anything different.”