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Nick Clegg told Liberal Democrat supporters they had won a "stunning victory" in Eastleigh, despite the "exceptional circumstances".
Prime Minister David Cameron said today that the Eastleigh by-election result was "disappointing" but he was "confident" that the Conservatives could win back support at the general election.
Liberal Democrat leader Nick Clegg has thanked party supporters after the party held the seat of Eastleigh in yesterday's by-election.
He said: "This has been a by-election we have had to fight in exceptional circumstances. Our opponents have thrown everything at us. We held our nerve, we stood our ground, we worked as a team, we went out and campaigned on every doorstep. We overcame the odds and won a stunning victory."
The UK Independence Party's Diane James, has described beating the Tories to take second place in the Eastleigh by-election was a "humongous" shock that represented a "seismic shift" in UK politics.
Conservative candidate Maria Hutchings polled 10,559 votes - more than 1,000 behind Ukip, which snatched huge chunks of the coalition parties' 2010 general election vote share, taking more than 27% of the total.
Conservative MPs have been tweeting after the party's candidate, Maria Hutchings, finished third in the Eastleigh by-election:
The Conservative Education Secretary Michael Gove told Daybreak that UKIP's success in the Eastleigh by-election is purely down to "protest."
He said: "People from Lib Democrat ranks and Conservative, were voting UKIP because they wanted to register a sense of pain and frustration at a difficult time for the country."
Liberal Democrat president Tim Farron has called the Eastleigh election the most "important by-election since the war."
His party's candidate Mike Thornton won the by-election with a majority of 1,771.
Speaking to Daybreak he said the win was an "outstanding" result, that speaks volumes about the Lib Dems' place in the next general election.
The Liberal Democrats are celebrating after Mike Thornton won the race to be MP for Eastleigh.
They fought off UKIP who came second - the party's best ever result in a by-election
The Conservatives came third while Labour came fourth.
The by-election was called after Chris Huhne resigned when he admitted perverting the course of justice.
The town has been in the spotlight over the last three weeks and the media were out in force at the election count last night.
Latest ITV News reports
Liberal Democrat leader Nick Clegg has hailed his party's success in the Eastleigh by-election.
Voters go to the polls today in the closely-contested Eastleigh by-election that is poised to heap pressure on the coalition Government.