A telephone poll by Survation showed the Conservative candidate Jill Mortimer on 49 per cent, followed by Labour’s Paul Williams on 42 per cent.
It follows the resignation of current MP Mike Hill after allegations of sexual harassment, which he denies.
His majority was slashed dramatically at the last election after the chairman of the Brexit Party Richard Tice ran and took a quarter of the vote.
In 2019 Labour won 37.7 per cent, the Tories 28.9 per cent, the Brexit Party 25.8 per cent, and the Liberal Democrats 4.1 per cent.
A Labour source said: "Labour would have lost Hartlepool in 2019 had it not been for the Brexit Party.
"In the context of the vaccine bounce, the Conservatives should take this seat."
The poll was commissioned by the Communication Workers Union, but spoke with just 502 voters.
The seat last returned a Tory candidate in 1959, an has been Labour since 1964.
A Tory source said: "The only poll that matters is the one on 6th May."
The Labour leadership also suffered a blow in the poll, with Sir Keir’s net favourability rating with his own voters just 30 in Hartlepool, compared to Boris Johnson’s rating of 80 among Tory voters.
The polling did however show support for left-wing policies, with 57 per cent wanting Royal Mail nationalised and 67 per cent backing investment in public services.
It also found that 69 per cent support free broadband for all households and businesses, a policy that formed part of Jeremy Corbyn’s Labour manifesto.
Dave Ward, the leader of the CWU, told The Times: "The fact that Hartlepool might elect a Tory MP for the first time since 1959 suggests to me that rather than rebuilding the red wall, Labour might be about to lose more of it.
"Working people want the real thing [...] politicians that have a moral backbone, that can tell you what they believe because it’s an integral part of who they are and not because it was approved by a focus group and a handful of the political elite.'"