The ICM poll in The Guardian newspaper put the SNP, which wants Scotland to leave the UK, on 43 per cent, which, if reflected at the ballot box, could leave the left-wing party as kingmakers in the London parliament.
It could also severely dent the centre-left opposition Labour Party's hopes of overtaking Prime Minister David Cameron's Conservatives and returning to power in the May general election.
The online poll of 1,004 adults put the SNP on 43 per cent (up from 20 per cent in the 2010 general election) in Scotland, with Labour on 26 per cent (down 16 per cent).
The SNP's membership has more than tripled to 90,000 since the September 18 referendum on Scottish independence, when 55 per cent of Scots voted to remain part of the UK.
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"We are prospectively looking at the collapse of citadels that have always been Labour since the 1920s," said Professor John Curtice of Strathclyde University.
"It is becoming clear that the independence referendum has reset all the dials," the electoral behaviour expert told The Guardian, calling it "the political transformation of a nation".
The ICM poll would give the SNP 45 seats and Labour 10, on a uniform swing.
Scotland is set to get sweeping new powers, including setting its own income tax rates, under plans unveiled last month by a cross-party commission on greater devolution set up after the referendum.
"More and more people are putting their trust in the SNP to stand up for Scotland's interests, and ensure that Westminster delivers the powers needed," said Angus Robertson, the SNP's general election campaign director.