Their rating increased from 12% to 20% between February and the end of last week.
The support has leaked from the SNP, whose backing dipped by six points to 26%, and the Tories, who dropped from 17% to 14%.
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Labour rose 2% to 36% in the poll, carried out by Ipsos MORI for a debate on STV last night featuring leading politicians from each of the four main parties in Scotland.
The figures emerged as nominations closed for the General Election with hundreds of candidates standing in Scotland’s 59 seats and as SNP leader Alex Salmond backed tactical voting in England which could benefit the LibDems.
Speaking at the launch of the SNP manifesto, he said: “Voting for the objective of denying Labour or the Conservatives an overall majority would be legitimate.”
Mr Salmond claimed a hung Parliament would be the “best thing for the people across these islands”. He said the SNP would not enter a coalition with any of the main UK parties but would look at issues on a vote-by-vote basis to try to extract concessions.
Labour’s Holyrood leader Iain Gray said there were “two massive credibility gaps” in the manifesto with “no mention of their economic policy and complete silence on who they want to be prime minister”.
Scottish LibDem leader Tavish Scott branded it a “true Alex in Wonderland performance” and Tory spokesman David Mundell said it contained no coherent economic plans to help Britain out of recession.
Meanwhile, three UK-wide polls show growing volatility in public opinion as the party leaders prepare for the second TV head-to-head debate tomorrow night.
A Comres daily snapshot gives the Conservatives a nine-point lead placing the Tories up three on 35%, the Liberal Democrats and Labour both down two points on 26%.
However, another daily poll by YouGov suggests the opposite, putting the LibDems up three on 34%, the Tories down two on 31% and Labour down one on 26%.
A Populus weekly snapshot puts the Conservatives just ahead on 32%, down four points, the LibDems on 31%, up 10, and Labour on 28%, down five.
Gray converts to LibDems
One of Scotland’s most acclaimed writers has been unveiled as a surprise convert to the Scottish LibDems as the party prepares to launch its manifesto today.
Alasdair Gray, the author of Lanark, hopes to help Katy Gordon defeat Labour’s Ann McKechin in Glasgow North. In recent years, the 75-year-old has divided his votes between the Scottish Socialists and the SNP.
He said: “The Labour Party in my opinion is at local, government and parliamentary level completely corrupted by its connection with finance and big business.”