Up to 100,000 building jobs could be lost.
The ICM survey for the Sunday Telegraph puts the party on 47 per cent of the vote with its nearest challenger, the Scottish National Party (SNP), on 33 per cent.
Liberal Democrats are on nine per cent and the Conservatives on seven per cent.
The poll, the first conducted within the rock-solid Labour seat, is a big boost for Gordon Brown.
Labour’s support has slumped since the 2005 general election when it won Glasgow East with a massive 61 per cent of the total vote, reflecting the string of political crises which have beset the Prime Minister, his government, and the Scottish Labour Party.
Nevertheless, the fact that Labour appears on course for victory will be a major relief for Mr Brown.
Party sources said they remained worried about levels of turnout in the seat and recognised a "lot of work still needs to be done" ahead of polling day on 24 July.