Theresa May is racing towards victory as Tory rivals attempt to derail her likely coronation by accusing her of lacking ther "moral authority" to be prime minister.
Polling has revealed that most Conservatives back the Home Secretary to replace David Cameron.
Ms May was backed by 60% of Tory voters, with Mr Gove second on 10 points and Mrs Leadsom on six, according to the ICM poll for The Sun on Sunday.
Among party members, who will vote to decide the winner of the leadership contest, some 46% say she would make the best prime minister.
Bitter recriminations over rival Michael Gove's decision to pull the rug from under Boris Johnson's leadership bid appear to have dented his prospects of taking on the Home Secretary in the final vote.
In an attempt to destabilise Ms May's campaign, Mr Gove says that she lacks the moral authortty to lead the country because she campaigned against Brexit.
"If you are going to have a leadership election and the prime minister has chosen to stand down, then the logic is that you need to have someone who backed Brexit and believed in it and argued for it as you leader in these negotiations," he told The Sunday Times.
The Justice Secretary faces being pushed into third place by fellow Brexit campaigner Andrea Leadsom, whose support is growing.
Former City worker Mrs Leadsom has likened herself to Margaret Thatcher and praised the late prime minister's ability to mix toughness with "personal warmth".
She also criticised any attempt to hand the leadership to Ms May.
"Some are suggesting the simplest way for the Conservative APrty to move forward is some sort of "coronation" and that there should be no role for those who campaigned for Britain to leave the EU.
"I can't believe anybody would seriously consider this," she told The Sunday Times.
Mr Gove has faced accusations of "treachery" since his decision to pull his support for Mr Johnson and stage his own bid for the top job.
He told the newspaper his confidence in the former London mayor had "evaporated".
"Over the past week, to my deep regret, my confidence evaporated. That led me to make the difficult decision, at no little cost, to put friendships aside and act in the national interest," he said.
With levels of support stronger than the combined total of her four rivals, Mrs May appears to be on course to take the keys to No 10.
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.
Although the poll puts Mr Gove, who has wider name recognition, ahead of Mrs Leadsom, bookies have slashed the odds on the junior minister making it through the knock-out stages in Parliament to go up against Mrs May in the head-to-head.
The first round of voting to whittle down the field of runners is being held on Tuesday.
More than half of those polled - 55% - by ICM 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% 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."
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