In a huge blow to the authority of the deputy prime minister, the Lib Dems were on course to lose all but one of the 11 seats they won in Strasbourg at the last election in 2009.
Catherine Bearder scraped home in the south-east of England as the party captured the penultimate seat in the vast constituency, just behind the Greens.
Party veteran Sir Graham Watson, the former leader of the Liberal grouping in the European parliament, was the biggest casualty of the night as he lost his seat in the south-west after 20 years in Strasbourg. The Lib Dem vote halved to around 7%.
The poor performance, worse than in the 1994 elections when it won two seats under the old first-past-the-post system, prompted renewed calls for Clegg to resign. Martin Todd, a member of the party's federal executive, told the BBC: "I am extremely concerned by what has happened. We have seen our share of support halve. There is a real issue with our strategy, there is a real issue with our leadership. Just saying more of the same just isn't going to cut it. I am really concerned that the initial response to what is a disaster is far too complacent."
A grim-faced Danny Alexander, the Lib Dem chief secretary to the Treasury who is Clegg's closest cabinet ally, said: "Apart from Catherine Bearder's election in the south-east it has been a pretty awful night for the Liberal Democrats. People have used European elections over many parliaments to have a go at the government in office."
Party MPs made little attempt to shy away from the party's poor performance. Tim Farron, the party president who is seen as a leading candidate on the left to replace Nick Clegg, said the results were as bad as he expected.
He told Sky News: "It's as bad as I feared and I'd hoped it would be better … If we had done that [avoided forming a coalition] we would have been in a healthier position tonight – we would have been recording several Liberal Democrat MEP successes, I am sure.
"Instead, we put the national interest ahead of our own. I am proud we have done the right thing. But we always knew it would be electorally damaging for us."
Farron spoke after the Lib Dems saw their MEPs fall in early results. The veteran pro-European Andrew Duff, who has represented the east of England, was one of the early casualties. That was shortly followed by the loss of the Lib Dem seat in the East Midlands – the constituency represented by Nick Clegg between 1999 and 2005.
Highlighting the significance of losing in the party's south-west heartland, Jeremy Browne, the former Lib Dem home office minister and MP for Taunton Deane, tweeted: "Graham Watson losing in the south-west is a serious blow and a sad loss."
The poor Lib Dem performance – at the lower end of expectations in an internal document leaked to the Guardian last week – will put immense pressure on the deputy prime minister. Activists leading the libdems4change website have published an open letter calling on Clegg to stand down. But by it had attracted just 268 signatures.
Supporters of Clegg have derided a push to oust the Liberal Democrat leader from office in the wake of disastrous local and European election results, claiming there were only minimal signs of a revolt inside the parliamentary party.
Ed Davey, the climate change secretary, said: "These have been disappointing results. But that is what people's expectations were, given the polls. I am just proud that we fought a positive campaign, made the case for Europe – Nick Clegg leading from the front, taking on the Eurosceptics.
"It may not have worked yet. This is the beginning of that argument. It is vital that that argument is made. But I am delighted and pleased that Liberal Democrats are making that argument."
But Clegg's critics, comprising more than 200 party activists who backed the call for a change at the top, say the deputy prime minister is offering no strategy to prevent electoral oblivion in 2015 other than the hope that the current message will be better received in a year's time.
They claim there will be further momentum when the party sees the scale of the setbacks in the European elections. Some of those calling for a change in leader would prefer Vince Cable, the business secretary, to take the helm without a contest, but it is unlikely that the Treasury chief secretary, Danny Alexander, or other key figures at the top of the party would permit such a coronation.
The group says it would only require quorate meetings of 75 constituency parties to trigger a leadership ballot, adding there was no need for any subsequent leadership election to turn into a bloody civil war. They include 45 sitting councillors, two council group leaders and 33 former councillors, including one former council leader. Another three prospective parliamentary candidates, 22 former parliamentary candidates and seven chairs of local parties are also signatories.
One backbench MP, John Pugh, claimed as many as 12 MPs wanted Clegg to step aside. But the deputy prime minister has retained the critical support of Farron. Writing on the Guardian's website, Farron defended the party's European election campaign: "Britain's interests will continue to be best served by staying within the European Union. Britain's interests will also be best served by standing by our decent, inclusive and tolerant values. And Britain's interests will therefore be best served by a courageous Liberal Democrat party led by Nick Clegg, standing apart from and ahead of the timidity of Labour and Conservatives."
Lord Ashdown, the former Lib Dem leader and the 2015 election campaign chairman, dismissed the calls for Clegg to go . "This idea that's been put about by these people who are calling for a leadership election is just about the silliest idea I've heard I think in my political career. It's just not serious politics."
Ashdown told BBC1's Sunday Politics that added that the signatories for the libdems4change letter were dwarfed by the 363 people who have liked the Lib Dems "Friends of Cake" Facebook page. He praised Clegg for having the courage to speak up in favour of the EU in the election campaign, though he added that his qualities were not yet appreciated by voters. On BBC1's Sunday politics, he said: "Nick Clegg...[is] a man of courage, of integrity, of decency, he's one of the, I think the best prime minister Britain hasn't got, though that hasn't got through to the electorate yet but in the context of a general election I believe it will. I'm devoted to the man and I believe he can do amazingly well in the general election, further than you think."
Ashdown spoke out after Pugh and Adrian Sanders became the first two Lib Dem MPs to question publicly whether it was right for Clegg to continue. Pugh told the Sunday Times: "Although I admire enormously Nick's bravery, it does not follow that because the captain should go down with the ship, that the ship has to go down with the captain."
Sanders said the party had a leadership problem that needed addressing. He added: "It won't be addressed if people remain silent. And it won't go away if people insult those brave enough to speak truth to power.
"Sadly those who refer to people wanting to see our support increase as 'numpties' lower the level of the debate as much as those who claim that defenders of the status quo are after peerages or other honours."
Andrew George, Lib Dem MP for St Ives, said it was "certainly not the right time" to change the leadership. George said he was not known for being obsequious to those at the top of the party but the current speculation about Clegg's future was "hardly registering in a teacup", let alone being a storm.
David Ward, the Lib Dem MP for Bradford East, said it would be "folly" to change leader before the next election but thought there had been a disconnect between the national party and its grassroots supporters.
The Lib Dems last week lost Kingston upon Thames council in west London after 12 years, delivering a warning to the local MP and cabinet minister, Ed Davey. And the party was estimated to have secured 13% of the vote in the local elections – a huge fall in its support at the 2010 general election.
The Liberal Democrats have now lost 1,369 seats in four rounds of local elections since 2011.
But opinion polls have suggested the party is on course to win a share of below 10% in the European elections, suggesting it is likely to see a dramatic reduction in the eleven seats it won in 2009. It could even fall below the Greens into fifth place. Ashdown countered that he could remember when the party support was so low it registered as an asterisk on polls.
In the face of such losses there was fury among some in the party at an email sent out in the name of the chair of the parliamentary party Annette Brooke on Friday night sent to party members claiming, "In our held seats, where we have strong and established campaigns, we're seeing some very good results. All of these results tell the same story - in many of our strongest areas we are winning elections."
Farron, reflecting on a net loss of 307 council seats, took a more sensitive tone, saying the party was hurt but that Clegg would lead the party into the general election.
Farron said, "There will be lots of people bruised by the results. The results have been disappointing. There were lots of people out there who did not deserve to lose. All the same across the country … we have seen the Lib Dems do well. Our job is to build those fortresses," he said.
Farron is understood to be keeping his powder dry until next year. He is being seen as the "wasteland candidate" – the person most likely to pick up the pieces if the Lib Dems suffer a huge defeat in the general election.
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