LONDON — UK Prime Minister Theresa May could soon be planning an overhaul of her team of top ministers in a bid to reassert her authority and end the government infighting that’s put Brexit talks in jeopardy.

Senior officials in Ms. May’s Conservative party, speaking on condition of anonymity, want her to deal with Boris Johnson, who has angered colleagues by forging his own path on Brexit in the run up to what proved a disastrous party conference for Ms. May this week in Manchester.

In an interview with the Sunday Times, Ms. May sent a strong signal about her intentions when asked specifically what she planned to do about her rebellious foreign secretary, the former London mayor who’s in the past been touted as a potential successor.

“It has never been my style to hide from a challenge and I’m not going to start now,” she told the newspaper. “I’m the PM, and part of my job is to make sure I always have the best people in my Cabinet.”

Ms. May faced fresh calls to quit following a chaotic speech at the conference that she almost failed to finish after a prolonged coughing fit. Grant Shapps, a former Conservative Party chairman, said on Friday he’s orchestrating a campaign to persuade her to step down — to which Ms. May responded by saying she’s providing the “calm leadership” the country needs.

Removing Ms. May now would throw Brexit negotiations into disarray. It would take as long as three months for the Tories to pick a new leader, and there are just 18 months to go until Britain tumbles out of the bloc. Ms. May made some concessions to Europe in a speech in Florence on Sept. 22, injecting momentum into long-stalled talks.

With negotiations to resume on Monday in Brussels and investors rattled by the never-ending Westminster soap opera, Ms. May is moving to restore order. The reshuffle, according to the Sunday Times, would take place after an Oct. 19-20 summit in Brussels where Ms. May will be hoping for a breakthrough few think possible.

Senior Tories from Home Secretary Amber Rudd to Environment Secretary Michael Gove have rallied behind her in recent days. Still, the Sunday Times, citing Tories it didn’t identify, said half her Cabinet want her to stand down in the next two years.

Concerned that Ms. May’s government will collapse before Brexit is complete, European Union negotiators have held more frequent back-room talks with the opposition Labour party, the Telegraph reported, citing people it didn’t identify. They want assurances Labour will honor deals made with the Conservatives, the Telegraph said.

Conservatives remain anxious after Ms. May led them into a failed election campaign earlier this year. Many believe she must quit before the next election, due in 2022, but worry that a leadership contest now will provoke an earlier vote that could result in a victory for Labour’s Jeremy Corbyn.

Mr. Shapps said about 30 lawmakers want a new Conservative leader and prime minister. That’s fewer than the 48 needed to trigger a leadership battle, so if Ms. May is determined to stay, she can — for now.

“We think the prime minister should stand aside now voluntarily so there can be a leadership election as soon as possible,” Mr. Shapps told Bloomberg in a phone interview. “It is clear that we need to have a reboot and that means it is time to move on.”

Ms. May, 61, responded to her critics in the Sunday Times interview: “One minute journalists are accusing me of being an ice maiden or a robot, then they claim I’m a weeping woman in dire need of a good night’s sleep. The truth is my feelings can be hurt, like everyone else, but I am pretty resilient.” — Bloomberg

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