That is despite the SNP’s lead over Labour narrowing from a previous survey.
The new survey for The Scotsman shows Labour on 29 per cent of the vote with 41 per cent of those polled intending to back the SNP.
The poll, conducted by ICM Research, came after another survey by the same polling company earlier this year showed Labour trailing the SNP by 19 points and set to win just 24 per cent of the vote in the European Parliament elections on 22 May.
However, the 12 per cent gap between the two main parties in Scotland would still see the SNP win the most number of MEPs and add to its tally of two Euro seats, with Labour retaining its two Scottish representatives in the parliament.
Backing for the Liberal Democrats plummeted from 6 per cent earlier this year to just 5 per cent in the latest poll of 1,000 voters – a result that would see the party lose its only MEP George Lyon, who won his seat at the last Euro elections in 2009 with 11.5 per cent of the vote.
Support for the Conservatives fell by one point to 13 per cent, although the party would retain its sole Scottish representative if the polling results were replicated on 22 May.
The poll that showed Labour narrow its polling deficit to the SNP by seven points was carried out before the party set out radical plans to devolve new powers to Holyrood with an increase in income tax for those earning £150,000 or more to 50p in the pound.
Anti-EU party Ukip saw its support fall from 7 per cent to 6 per cent, ahead of the Lib Dems but still well short of the support needed to secure the election of an MEP. The Scottish Greens were on 4 per cent of the vote.
The ICM poll also showed that support among Scots for pulling out of the EU has fallen, with fewer than a third stating they would vote to leave Europe in the referendum Prime Minister David Cameron has pledged to hold if the Conservatives win next year’s general election.
The research showed that 14 per cent of Scots said they would probably vote to leave with 16 saying they would definitely back an EU exit.
A previous Scotsman poll showed that 15 per cent of those polled said they would “definitely” vote to leave the EU, with 19 per cent saying they would probably vote for UK withdrawal. However, in the latest survey there was a slight increase in the number of Scots who intend to vote against the UK leaving the EU with 25 per cent saying they would “definitely” vote to stay and 22 per cent stating they would “probably” vote to remain in Europe.
SNP business convener Derek Mackay MSP last night said: “This is a remarkable poll – after nearly seven years in government, the SNP are still far and away Scotland’s most popular political party, and in a strong position as we approach the European elections.
“The European elections will be a fantastic opportunity to stand on the SNP’s positive message of an independent Scotland playing a constructive role at the heart of Europe – in contrast to Westminster threatening isolation through an in/out referendum.”
However, the increase in support for Labour comes after the party defeated the SNP in the Cowdenbeath and Dunfermline by-elections this year.
A Scottish Labour spokesman suggested the party was in a stronger position than at the last Holyrood election, when it suffered one of its biggest ever defeats at the hands of the SNP.
The party spokesman said: “We are aiming to build on the by-election successes of Dunfermline and Cowdenbeath and will continue to put forward the case for Scotland remaining within a strong UK.”
A spokesman for the Scottish Liberal Democrats dismissed suggestions that the party was facing another electoral meltdown in Scotland – three years after its representation at Holyrood was reduced to five MSPs.
He said that the planned televised debate between Deputy Prime Minister Nick Clegg and Ukip leader Nigel Farage ahead of the Euro elections would help boost support for the party in Scotland.
The Scottish Conservatives declined to comment on the findings.