With levels of support stronger than the combined total of her four rivals, the Home Secretary appears to be on course to take the keys to No 10.
Mrs May was backed by 60 per cent of Tory voters, with Michael Gove second on 10 points and Andrea Leadsom on six, according to the ICM poll for The Sun on Sunday.
Among party members, who will vote to decide who wins the leadership contest, some 46 per cent said she would make the best prime minister.
Mrs May has also been backed by more MPs, who select the final two candidates to go on to the ballot paper, than any of the other candidates.
The poll puts the Justice Secretary ahead of Mrs Leadsom, despite bookies slashing odds on the Energy Minister becoming the favourite to go up against Mrs May in the final vote.
More than half – 55 per cent – were unable to give any view on Mrs Leadsom or Work and Pensions Secretary Stephen Crabb, who have lower profiles than the long-standing Cabinet ministers, and 42 per cent had the same problem with former frontbencher Liam Fox.
ICM director Martin Boon told The Sun on Sunday: “The race to replace David Cameron might turn from a marathon into a sprint judging by these results. Theresa May is blasting out of the blocks and leaving her fellow competitors for dead.
“She is overwhelmingly seen as the most competent candidate by both men and women, in every region of the country and among supporters and members of all parties.”