The new Opinium survey found 42% intended to vote for Labour, with the Tories on 39%.
It is the first time Labour has been ahead of the Government since early July 2019, when Theresa May’s time in office was coming to an end.
In a boost for Mr Starmer, the poll, for the Observer, also suggested 55% of voters believe he is ready to be Prime Minister, compared to 36% who said the same for Mr Johnson.
Meanwhile, 40% believe Labour is ready to form the next Government, compared to 36% in July.
In a fresh headache for the PM, disapproval of the Government’s handling of the crisis reached its highest level since March, with exactly half (50%) disapproving – a net of -20.
Despite his latest announcement, 45% think the government is underreacting to the crisis, while 30% think they are acting proportionally and 20% think they are overreacting.
Adam Drummond, head of political polling at Opinium, said: “The Labour Party has finally caught up with its leader in polling.
“While this is the first time since Boris Johnson became prime minister that Labour have been ahead of the Conservatives on vote share, Keir Starmer has had better approval ratings (both raw and net) than the prime minister for some time and the two leaders have tended to draw on the question of who would be the better prime minister.
“Now the Labour leader has pulled ahead on that measure as well, leading the prime minister by 36% to 32%.
“While there is strong public support for the new Covid restrictions announced by the government earlier this week, they have not yet resulted in the sort of boost in the government’s approval rating that the initial lockdown measures brought in March, suggesting that the ‘rally around the flag’ effect was a one-off.”
Opinium carried out an online survey of 2,002 UK adults from September 23-25.