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David Lammy has come out in support of the prime minister, saying Keir Starmer would fight in a leadership contest after Andy Burnham said he would join one if elected an MP.

“There is no contest at the moment, and my view is it would be a huge distraction at this time,” the deputy prime minister told LBC this morning.

“The prime minister, by the way, has been absolutely clear: if there is a contest, he’ll be in it.”

He added: “I’ve supported every leader of the Labour party. They’ve had my full loyalty. Keir Starmer has got my loyalty, full loyalty, until the day he no longer wishes to serve.”

His remarks came after the Greater Manchester mayor announced he would challenge the prime minister should there be a leadership race. It was the first time Burnham, who is standing in the Makerfield byelection, has publicly said he would consider launching a bid to become the Labour leader.

Appearing on Question Time last night, he said: “I think Wes Streeting seems to have launched a leadership contest, so if that is running, I would seek to join it. But I’d have to persuade members of the Parliamentary Labour Party to do the same.”

Hitting back at Burnham, Downing Street issued statement saying Starmer “will not walk away”, adding: “The country expects us to focus on governing and to deliver change for hard-working people, not get distracted by Westminster debates.”

In an interview with the Guardian’s political editor Pippa Crerar, Burnham signalled he would begin transforming England’s broken social care system this year if he became prime minister.

“It is urgent, the need to fix social care, and I personally would look at all of the kind of implications of that in relation to inheritance tax and care charges and everything. I wouldn’t flinch from it,” he said.

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Also today, Lammy said tech billionaire Elon Musk should “step back” from tweeting about the murder of Henry Nowak amid an ongoing feud between the government and X owner.

“I think there’s an IPO this week in the States on Starlink. Elon Musk should get on with that,” Lammy told Sky News.

“I mean, tweeting over 100 times about this tragic, horrific case … I urge Elon Musk to stay out of tweeting about this sensitive case.”

He added: “I don’t spend time on X surfing Elon Musk tweets, so I haven’t read them, but I’m not sure any of them reached the standard that require that. But I think it is appropriate for politicians to urge Elon Musk to step back.”

Starmer has accused Musk of “interfering in our politics” and attempting to create division with the numerous social media posts he has made about the murder of Nowak, many of which have used far-right themes and talking points.