Among all voters, support for Corbyn as prime minister was just 14 per cent, with May securing about three times that level at 47 per cent.
The figures come from an Opinium survey carried out for The Observer newspaper.
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The poll also shows the general Tory lead over Labour falling to nine points, with the Conservatives down three per cent to 38 per cent, and Corbyn’s party up one to 29 per cent.
Meanwhile, Ukip had 14 per cent and the LibDems just seven per cent.
However, a separate ComRes poll for the Independent and Sunday Mirror put the Tories at 46 per cent, with Labour on 25 per cent, the Lib Dems on 11 per cent and Ukip on nine.
The findings come as Corbyn faces renewed attacks on his leadership ahead of next month’s local elections.
At a by-election in Middlesbrough, the party lost a council seat to the Tories thanks to a swing of eight per cent.
Labour’s Middlesbrough South and East Cleveland Tom Blenkinsop MP, a vocal critic of Corbyn, blamed the leader for the local loss, saying: “We lost due to the leader’s name being mentioned on the doorstep as the reason why residents were not voting Labour.”
According to the Observer poll, 35 per cent of people said the Tories were most trusted to lead Brexit negotiations, compared to 12 per cent for Labour.
Health and Brexit remained the most important issues among voters, but terrorism climbed from fifth to third place in the aftermath of the attack at Westminster.