* Win for seat in southern England buoys party
* Newspaper poll puts Liberal Democrats in fourth place
* Leader Clegg says determined to stick to austerity
By Tim Castle
BRIGHTON, England, March 10 (Reuters) - Britain's junior coalition partners, struggling with falling poll ratings, promised voters on Sunday that winning a vote for a parliamentary seat was proof it was ready for a comeback.
The coalition, led by Conservative Prime Minister David Cameron, has been hard on the Liberal Democrats, out of power for generations until its creation following an inconclusive national election in 2010.
Left-leaning voters have abandoned the party, arguing it has betrayed its core values. The breaking of a pledge to abolish university fees compounded the damage, cutting poll ratings by more than half the 22 percent gained in 2010.
A sex scandal over a former senior party figure and a court case involving a former minister have also dented its reputation.
A nationwide poll in the Observer newspaper on Sunday put the Liberal Democrats in fourth place on 8 percent, behind the right-leaning UKIP on 17 percent, Cameron's Conservatives on 27 percent and opposition Labour on 39 percent.
But winning the seat for Eastleigh, southern England, has buoyed the Liberal Democrats and piled pressure on Cameron, whose party was beaten into a humiliating third by the anti-EU UKIP, which has no seats in central government.
Speaking at a party conference in the south coast city of Brighton, Clegg urged Liberal Democrats to seize the momentum and make their voices heard.
"I have spent nearly three years urging you to hold firm ... to remain steady under fire," Clegg said. "Today I have a different message for you - win. Get back out there. Tell our side of the story. And we will win again."
In a defiant message, Clegg highlighted his party's determination to stick to the coalition's austerity programme, blamed by the opposition Labour party for weakening an economy close to its third recession in four years.
"Countries around the world face the same, hard truth - we must all pay the piper in the end. I want to make one thing clear - we will not flinch on the deficit," he said.
The conference comes after a difficult period for Clegg's party. Former Liberal Democrat cabinet minister Chris Huhne resigned on Feb. 4 after admitting covering up a speeding offence.
The sex scandal that has ensnared Chris Rennard, the party's former chief executive, has also raised questions for Clegg about what he knew about it. Rennard denies the accusations.
But in Brighton, the mood was optimistic and officials believe that after the Eastleigh victory the tide has turned, and many expect that to be shown in local elections in May.
"For the first time in a generation we could campaign on our record of local delivery and our record of national delivery too," Clegg said.
Observers were cautious about the party's fortunes at the next election in 2015. A separate poll released at the weekend forecast the Liberal Democrats would lose more than half its 57 seats in the 650 seat parliament if a vote were held now.
"They are going to find it very hard at the next general election," said Manchester University politics professor Andrew Russell. "There are some very high profile (Liberal Democrat)politicians who could be casualties. While they won't be wiped out, they are going to find it very tough." (Editing by Maria Golovnina and Alison Williams)