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The study carried out by YouGov spoke to 1,068 adults between June 3 and June 7, finding 34% of decided voters backed Sir Keir Starmer’s party, compared to 30% for the SNP.
The last poll from the firm in May found the parties on 39% and 29% respectively, but the gap has since shrunk.
Elsewhere, the Scottish Tories increased by one point to 13%, while the Lib Dems remained on 8%.
Reform UK also overtook the Scottish Greens, rising from 4% to 7%, while the SNP’s former coalition partners dropped one point to 6%.
The poll found that more than one third of voters who backed the SNP in 2019 will vote for another party, with 24% saying they will back Labour.
Meanwhile, the Tories could lose more than half their voters from 2019, with just 49% saying they would back the party again, with 19% turning to Labour, 18% to Reform UK and 10% to the Lib Dems.
The poll also found that 53% of decided voters would vote against Scottish independence, down two points from the last poll, while support for separation increased by two points to 47%.