Half of Tory members think Kemi Badenoch should not lead party into next election

However, three in five said she was doing a good job as leader in the survey released during the Conservative Party conference.

The party has been determined to demonstrate unity despite its polling difficulties and questions about Mrs Badenoch’s leadership.

Of those polled, 50 per cent said she should not be the party’s prime ministerial candidate in 2029, while 46 per cent said she should.

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Most thought she was doing a good job as party leader, at 61 per cent compared with 37 per cent who said she was not.

Shadow justice secretary Robert Jenrick would be the favourite to succeed her if she stepped down in the next few months, with 37 per cent saying he would be their top choice.

The former leadership contender has insisted he is backing Mrs Badenoch.

Asked during a fringe event on Monday whether he would stand for the party leadership should there be a vacancy, he said: “There isn’t a vacancy and I don’t expect there will be.

“My expectation is that Kemi will lead this party into the next general election.”

The next most popular choice was Boris Johnson, with 22 per cent picking the former prime minister, and 20 per cent favouring shadow housing secretary James Cleverly, who was a contender for the leadership last year.

An electoral pact with Reform UK proved popular among the group, with 64 per cent saying they would support an agreement between the two parties not to stand candidates against each other in target seats.

But they were split on a full merger, with 46 per cent in favour while 48 per cent were opposed.

YouGov polled 652 Conservative Party members between September 26 and October 2.