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Liberal Democrat leader Nick Clegg has responded to election results after UKIP gained at least 88 county councillors, and the Liberal Democrats secured just 352 votes at South Shields.
Mr Clegg defended the result saying that the party was "on a journey" from being a "protest party" to a "government party".
David Miliband, who triggered the South Shields contest when he decided to quit as an MP, congratulated Labour's Emma Lewell-Buck, who won the seat with a reduced majority of 6,505.
Liberal Democrat party president Tim Farron has described the result in South Shields as "shocking" for his party, but insisted the outcome did not represent the whole picture.
Mr Farron told the BBC Radio 4 Today programme:"The Westminster battlegrounds are where it is at and for the Lib Dems, South Shields is one extreme where we have got little strength on the ground and have been obliterated.
"Then you look at other places like Cheltenham, Taunton, Eastbourne, hopefully west London, places like West Dorset where we have got to win at the next election where we are doing extremely well.
"Most of our battles are against the Tories and against the Tories we are doing very well."
The Liberal Democrats fell to seventh in the South Shields by-election with Emma Lewell-Buck retaining the seat for Labour.
Lewell-Buck became the first woman MP for the constituency with a majority 6,505, claiming more than 50 percent of the vote:
Independent candidate: 1,311
Independent Socialist Party: 750
Liberal Democrats: 352
Monster Raving Loony Party: 197
Independent Candidate: 57
UKIP leader Nigel Farage told Daybreak that today's result in South Shields was "remarkable".
He said: "People haven't seen us as being relevant for local elections, or in some ways general elections, so for us to be scoring at least 26% of the vote where we stand is, I think, very significant indeed."
When asked about whether the party had now entered a four-party race, Mr Farage replied: "Numerically we're the third [party] because the Lib Dems are trailing behind."
He added: "This wave of protests certainly isn't short term, it's lasting."
Deputy Liberal Democrat leader Simon Hughes has congratulated Labour on their South Shields win.
The Lib Dems came seventh place in the by-election, speaking to Daybreak Mr Hughes said, "the Tories were always the challengers and they've been knocked out by UKIP."
He added: "We appear to be doing well in our territory and not giving that up."
Hilary Benn MP for Labour told Daybreak he was "delighted" for Labour candidate Emma Lewell-Buck's win in South Shields.
He said: "It's a really good solid result."
UKIP pushed the Tories into third place, collecting 24.21% of the votes, Mr Benn added, "UKIP have clearly done very well, it's a part of protest and times are really tough."
As she won the South Shields by-election, Labour's Emma Lewell-Buck said the coalition Government was taking the country in the wrong direction.
In her maiden speech, she said: "Mr Cameron, when working families need a Government on their side, you made them pay for a tax cut for millionaires."
Former Liberal Democrat MP Lembit Opik described the South Shields result as "appalling" and demanded a "credible explanation from Nick Clegg regarding the recovery strategy".
The Lib Dems secured just 352 votes.
Mr Opik lost his Montgomeryshire seat in 2010.
Latest ITV News reports
Labour comfortably held the seat of South Shields after a by-election marked mainly by UKIP's success and the dire failure of the Lib Dems.