The darling of the Tory right is now the public’s second favourite as the “best prime minister”, should the current, besieged occupant of No 10 be forced out.
Men and voters over the age of 55 in particular are warming towards the outspoken critic of Ms May’s Brexit policy, the polling by BMG Research shows.
The results come as the public remains dissatisfied with the Prime Minister and amid persistent speculation that she will face a vote of no confidence from Tory MPs.
Meanwhile, Mr Rees-Mogg has put himself at the head of the growing Brexiteer revolt against Ms May, warning she has “failed” in her handling of the exit talks.
The 48-year-old has appeared to position himself as a leadership contender by saying the Prime Minister does not appear to be having “fun” in her job, while attacking her “gloomy” 2017 election campaign.
Mr Rees-Mogg has said it would be “very difficult” for him to become Prime Minister – as a father of six – but has notably failed to rule it out.
The poll finds that Boris Johnson remains the public’s favourite of the crop of Tory politicians who could succeed Ms May if she was forced to step down, on 13 per cent of voters.
But Mr Rees-Mogg is now second on 7 per cent, ahead of Mr Hammond (5 per cent), Ms Davidson (5 per cent), Ms Rudd (4 per cent) and David Davis, the Brexit Secretary (3 per cent).
More than half of voters (51 per cent) say they are dissatisfied with Ms May’s leadership, with only 33 per cent happy with her performance.
Meanwhile, both wings of the Tory party have warned a vote of no confidence in her leadership is nearing because of her fudging of her Brexit plans and failure to set out domestic reforms.
The vote will be triggered if 48 Conservative MPs send letters to Graham Brady, the chairman of the backbench 1922 Committee, who has refused to say how many he has received.
However, asked “which of the following Conservative politicians would make the best UK Prime Minister”, should Ms May fall, 57 per cent replied “none of the above”.
And Mr Rees-Mogg – dubbed “the member for the 18th century” by some fellow MPs, because of his old-fashioned persona – is becoming less popular among women and younger voters, the results show.
The poll shows that the Tories and Labour remain neck-and-neck in the public eye, with both on 40 per cent excluding don’t knows and those unlikely to vote.
The public is also dissatisfied with Jeremy Corbyn’s leadership – by 43 per cent to 34 per cent – and narrowly prefers Ms May in Downing Street, by 32 per cent to 30 per cent.
Source Note: BMG Research interviewed a representative sample of 1,507 GB adults online between 6-9 February. Data is weighted. BMG are members of the British Polling Council and abide by their rules
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