The Conservatives and Labour suffered heavy losses, with the former expected to get less than 10% of the vote.
Brexit Party leader Nigel Farage said he was ready to “take on” the Tories and Labour in a general election.
So far, Mr Farage’s party has won 29 seats, the Lib Dems 16, Labour 10, Greens seven, the Tories four, the SNP three and Plaid Cymru one.
Mr Farage told BBC Radio 4’s Today programme: “With a big, simple message – which is we’ve been badly let down by two parties who have broken their promises – we have topped the poll in a fairly dramatic style.
“The two party system now serves nothing but itself. I think they are an obstruction to the modernising of politics… and we are going to take them on.”
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The deputy leader of the pro-Remain Liberal Democrats, Jo Swinson, said the result should “give hope to all of the people out of there who want to stop Brexit”, and that they “should not be giving up without a fight”.
“When there is such a general shambles over Brexit, then [a further referendum] is the best way out of the impasse,” she told Today.
Polling expert Sir John Curtice said the results showed just how polarised the country had become.
Prime Minister Theresa May tried three times to secure MPs’ backing for her Brexit plan and resigned as prime minister after her fourth attempt prompted a big backlash.
She tweeted disappointment about the result for the Conservatives.
All 28 EU member states are electing MEPs to the European Parliament – the EU’s law-making body. Overall, the big centre-right and centre-left blocs lost ground, amid a surge in support for liberals, Greens and nationalists.
The UK had been due to leave the EU on 29 March, but when that deadline was missed, participation in the election became mandatory.
The Brexit Party topped the polls in every region of England apart from London. It also dominated in Wales, with Plaid Cymru second.
It has now become the joint largest national party in the European Parliament, alongside Germany’s CDU/CSU party.
The Brexit Party came in second place with a significantly lower percentage – 14.8% – followed by the Lib Dems with 13.9% and the Tories with 11.6% – meaning each party has one seat.
But Labour only received 9.3% of the vote – a loss in vote share of 16.6% – leaving it with no MEPs in Scotland for the first time.
Meanwhile, Northern Ireland’s count does not begin until Monday, with the results expected on Tuesday.
The night at a glance
- The UK is electing 73 MEPs, and 10 out of 12 regions have declared so far
- The Brexit Party has received the highest share of the vote in nine of the 10 regions – with 32% overall
- The Conservative Party has been widely rejected by the electorate, coming in fifth place
- The Lib Dems have taken second place with 20% of the vote – a vote that is clearly much higher in areas that backed Remain. In London, the Lib Dems came first and the Tories fifth
- The Labour Party has fallen to third place overall – fifth in Scotland – and is on course to end up with less than 15% of the vote, an even worse performance than their previous low in 2009
- The Green Party has also made gains, seeing its best performance since 1989
- Newly-formed Change UK has not won any seats, while UKIP has also haemorrhaged support to The Brexit Party – both have gained about 3% of the vote
The Tory story
Brexiteer and Conservative MEP for the South East Daniel Hannan – one of only three Tory MEPs elected so far – said it was his party’s “worst ever result”.
“We voted to leave (the EU) and we haven’t left – it’s that simple,” he told the BBC.
Tory leadership hopeful and former Foreign Secretary Boris Johnson said the public had delivered “a crushing rebuke” to both major parties for failing to deliver Brexit.
Prominent Brexiteer and Tory backbencher Steve Baker said his party faced “obliteration” if they did not get on with leaving the EU as they had pledged.
He told BBC Breakfast: “It is a grave time for our party and country, [but] I am not surprised that [the result] is as bad as it is. You just can’t break promises you have made like this and expect to go unpunished.”
Labour leader Jeremy Corbyn is facing increasing pressure from senior members of his party to back another referendum on Brexit, with his own shadow chancellor saying it is the only way through the deadlock.
John McDonnell said the country was now facing the prospect of a “Brexit extremist” becoming the next prime minister, meaning the UK faced the prospect of no deal.
“Of course we want a general election,” he said. “But realistically, after last night, there aren’t many Tory MPs who will vote for an election, it will be like turkeys voting for Christmas.
“If there can be a deal, great, but it needs to go back to the people. If it’s a no-deal, we’ve got to block it and the one way of doing that is going back to the people and arguing the case against it because it could be catastrophic for our economy.”
Labour’s deputy leader Tom Watson said the party needed to “urgently” rethink its Brexit position after the “disastrous” election results, while Emily Thornberry told the BBC that the party should call for another vote and campaign to remain.
But the leader of the Unite Union, Len McCluskey, said Labour’s attempt to “unite the nation” over Brexit was “an honourable objective that must not be abandoned”.
He added: “This is the time to hold our nerve because the true prize is the very real possibility of a looming general election.”
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Mr Corbyn told the BBC: “What you have from me today is a commitment that our party is listening to its members and its supporters, and reaching out to parties across the House of Commons to prevent a crashing out… with no deal.
“A commitment that the future will of course be put to a public vote, as we have proposed in Parliament.
“Any final deal has to be put to a public vote and that we are prepared to do.”
Big gains for smaller parties
In contrast to the two biggest parties, some of the smaller ones with an unambiguous message on Brexit were rewarded.
Anti-Brexit parties – those in favour of another referendum – collectively took about 40% of the vote, compared with 35% for the two parties in favour of leaving the EU without a deal.
Green Party co-leader Sian Berry said the case for a further referendum was stronger than ever, adding: “Giving the people the final say over the country’s direction is now clearly the only way forward, the way to draw a line under the Brexit chaos.”
Change UK failed to win any seats in the election, but leader Heidi Allen told the BBC her party – newly formed from ex-Labour and Tory MPs – was “down, but we are not out”.
Meanwhile, UKIP lost all its MEPs in the election, and saw a fall in its vote share of over 24%.
The party’s former deputy leader, Mike Hookem – who lost his seat in Yorkshire and the Humber – blamed UKIP leader Gerard Batten for the result.
He specifically highlighted Mr Batten’s association with former EDL leader Tommy Robinson – real name Stephen Yaxley-Lennon – who also failed to win a seat in the North West Region.
Were these results an overwhelming cry for us to leave the EU whatever the cost? Or a sign, with some slightly convoluted arithmetic, that the country now wants another referendum to stop Brexit all together?
Guess what, the situation is not quite so black and white, whatever you will hear in the coming hours about the meaning of these numbers.
The Brexit Party’s success was significant and Nigel Farage’s new group is the biggest single winner.
But the Lib Dems, Greens, Plaid and SNP – all parties advocating the opposite – were victors too.