Among all voters, support for Corbyn entering Downing Street slumps to 14%, with May given the nod by 47% in a head-to-head contest, an Opinium survey for The Observer finds.
More than a quarter of those questioned, 28%, said they wanted neither leader in Number 10.
In another blow to Corbyn, the poll puts the Tories ahead on all key issues, apart from the NHS.
The findings come as Corbyn faces renewed attacks on his leadership ahead of next month’s local elections after Labour lost a Middlesbrough council seat to the Tories in recent days on a by-election swing of 8%.
Labour MP for Middlesbrough South and East Cleveland Tom Blenkinsop, a strong critic of Corbyn, said: “We lost due to the leader’s name being mentioned on the doorstep as the reason why residents were not voting Labour.
“And I am certain this is not just the case here but across boroughs and constituencies the length and breadth of Great Britain.”
When asked which party was most trusted to lead Brexit negotiations, 35% backed the Conservatives, the same as last month, while Labour’s rating stayed static on 12%, the newspaper poll said.
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.
Labour, on 28%, enjoys an eight-point lead over the Tories when it comes to the NHS, but Corbyn’s party was named by just 7% as having the best policies on immigration - the fourth most important issue to those questioned.
The survey found the Tories had lost their double-digit lead in voting intentions, but remained a comfortable nine points ahead of Labour.
Opinium Research carried out an online survey of 2,002 UK adults aged 18 and over from April 11-13 2017. Results have been weighted to representative criteria.