Analysis of the impact of Brexit by former Tory donor Lord Ashcroft found Mrs May had a 37-point lead over the Labour leader, as 55% of respondents preferred Mrs May as prime minister compared to Mr Corbyn (18%).
In a further blow to Mr Corbyn's leadership, only four in 10 (38%) Labour voters chose him over Mrs May while 89% of Conservative voters backed their party leader.
The poll of more than 10,000 UK adults revealed people were closely divided over whether leaving the EU would make the UK better off (42%) or worse off (40%).
Nearly half (45%) of voters, including more than one third of Remain voters, said the Tories best represented their view of how the UK should handle Brexit and what the UK's future relationship should be.
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Voters of all parties favoured prioritising immigration control over access to the single market by 42% to 34% and Leave voters by 66% to 13% in favour of controlling immigration.
Brexit was seen as the most important issue for the country as a whole by both Leave and Remain voters, however only 39% of respondents said the EU negotiations were one of the top three issues for their families compared to the NHS (58%) and the cost of living (53%).
Tory voters were the most likely to stick with their party regardless of how they voted in the EU referendum, with 83.8% of Tory Leave voters and 76.6% of Remain voters planning to back the party again.
Seven out of 10 (71.5%) of Labour Remain voters and six in 10 (64.5%) Labour Leave voters would vote the same way, dropping to 68.4% and 54% respectively among Liberal Democrat voters.
:: A total of 10,153 adults across the UK were interviewed online between March 21 and 28 for the poll.