Labour is on 42 per cent, three points clear of the Conservatives on 39 per cent, according to an Opinium survey for the Observer.
In a sign of growing disquiet over the Government’s handling of the crisis, the opposition party has closed a 26-point lead that put the Tories on 54 per cent at the end of March.
It comes as the PM faces an extraordinary rebellion over Downing Street’s “rule by diktat”, with dozens of Tory MPs lining up to back an amendment by Sir Graham Brady, chair of the powerful backbench 1922 committee.
The amendment, facing a crunch vote on Wednesday, calls for Commons debates and votes on any Covid-19 measures before they are imposed.
Labour, the Lib Dems and the Scottish National Party all indicated they may lend the vote cross-party support. Combined with the 46 Tories understood to already be behind it, this would defeat the Government by three.
The poll also suggested 55 per cent of voters believe Sir Keir is ready to be prime minister, and 40 per cent believe Labour is ready to form the next government.
It is the latest poll to suggest unease among voters at Mr Johnson’s handling of the coronavirus crisis.
In the early stages of the pandemic, 65% of voters surveyed backed the Government’s handling of Covid-19, but the latest poll suggested only 30% now approve.
Tory whips were reportedly trying to placate rebels this weekend by bringing forward a debate on the already-imposed “rule of six” from early next month to this week, in a partial climbdown.
But Mr Brady said this would not be enough, after the PM announced sweeping 10pm pub curfews and a threat of Army involvement earlier this week to tackle the UK’s surging rates of coronavirus.
The backbencher told the Observer: “It is essential that the House of Commons should have the opportunity to debate and vote on emergency measures before they come into force.”
It came as an exclusive poll for the Standard found two-thirds of the country are pleased with the way Rishi Sunak is doing his job as Chancellor, in another sign the young Tory is in the ascendancy towards Number 10.
The Ipsos MORI poll, taken before the successful Jobs Support Scheme announcement, found 64 per cent say they are satisfied with his performance, while just 21 per cent are dissatisfied.
The only Chancellor to have done better since Ipsos MORI began asking the question in the 1970s was Lord Healey, one of the most popular politicians in modern times. He scored 67 per cent satisfied in 1978.
The architect of Eat Out to Help Out is leaving the PM behind on key image ratings for a potential PM including being “good in a crisis” and having “sound judgment”, pollsters Ipsos MORI discovered.