Labour have managed to claw back eight percentage points from the Tories, but still lag behind Theresa May's party by 16 points, according to a Kantar Public poll.
According to the survey, the Conservatives have slipped four points to 44% from last week, while Jeremy Corbyn's party are up four points to 28%.
Elsewhere, the Lib Dems are maintaining their position as the number three party with 11%, while Ukip stand at 8%.
With less than a month to go until the General Election, the poll found 11 % of voters had not yet made up their minds.
Luke Taylor, Head of Social and Political Attitudes at Kantar, said: "While one-in-10 likely voters have yet to decide how they will vote, it seems unlikely that these individuals will swing the electoral balance towards the Labour party.
Those that have not expressed a voting intention are currently more likely to associate Theresa May than Jeremy Corbyn with being a good negotiator, being decisive and having good attention to detail.
"These skills are likely to be important to voters because they know they are not just voting for a party but, indirectly, for a Prime Minister to negotiate the UK's exit from the EU. The recent campaign appearances from Theresa May suggest that she has cottoned on to this fact."
The polls arrived as leaders embark on their election campaigning, with May announcing she would consider bringing back fox hunting if elected prime minister and Corbyn delivering his campaign launch speech in Manchester.
The poll was conducted between 4 and 8 May and involved 1201 participants.