In a major boost for Jeremy Corbyn, the ICM survey for the Guardian puts Labour on 41%, up two points from a fortnight ago.
The Tories slipped one point to 40%, with the Lib Dems on 8%, Ukip on 5% and the Greens on 3%.
Meanwhile the Prime Minister’s lead over the Labour leader on who is best suited to reach a good Brexit deal has dropped to just eight points, having sat at 16 points in January and a massive 34 points before last year’s general election.
According to the poll, just 26% of the public now back the Prime Minister, compared to 18% for Mr Corbyn – a change from 35% and 19% respectively at the beginning of this year.
However 44% of those polled replied “neither” when asked which leader they rated best on the issue.
ICM pollster Alex Turk said: “The public’s trust in Theresa May being able to negotiate a good Brexit deal for the UK has collapsed.
“It used to be the second strongest area for May compared to Corbyn on the areas we’ve tested, beaten only by protecting people from threats at home and abroad, but now it falls to her fourth strongest area.
“It wasn’t too long ago – back in May 2017 – that almost half (47%) of the public trusted May most to do the best job of negotiating Brexit.
“To see this proportion collapse to just over a quarter (26%) on what’s considered the biggest issue of the day could explain some of the pressure exerted on her leadership coming from within her party in recent weeks.
He added: When couched in terms of negotiating Brexit, there seems to be a public appetite for someone else entirely. We’ve seen those who trust neither May nor Corbyn to negotiate a good Brexit deal jump from 31% in January to 44% in this poll.
“This now means that, more than in any other area we ask, a large slice of the British public tend to trust neither May nor Corbyn on Brexit.