A minister said Labour MP Richard Burgon has “never supported this Prime Minister.”

Asked about the Left-wing backbencher predicting Sir Keir Starmer would no longer be in No 10 after the May elections, Baroness Jacqui Smith told BBC Breakfast: “Richard Burgon has never supported this Prime Minister.

“He actually had the whip removed from him for a period of time because of his failure to support the Government, so the fact that he now thinks the Prime Minister should go is not actually new news.”

Asked if she thought Greater Manchester Mayor Andy Burnham would do a better job as leader, she said: “No. I think the Prime Minister is doing a good job.

“Of course Andy isn’t in Parliament, he’s doing a really good job as Mayor of Greater Manchester and actually when I talk to Andy what we tend to talk about is how can we make sure young people are getting the skills they need in Manchester, how can we support him to provide more opportunities… for the people of Greater Manchester.”

A minister denied that the Unite the Kingdom march over the weekend and Reform UK’s success in polls have played a part in the timing of the returns agreement under which detained migrants will be deported to France.

The “one in, one out” agreement with Paris saw the first migrants detained on August 6 and it is understood the first flight could be as early as Monday.

Asked if the rally and the fact that Reform UK were ahead of the Labour Party in the polls played a part in the timing of the start of the agreement, skills minister Baroness Jacqui Smith told Sky News: “No, this is something that we’ve been working on ever since we came into government.”

She also said: “We’re not going to be talking about the details of which flights and how many but it is starting in the near future.”

Sir Keir Starmer “very quickly” made the decision to sack Lord Peter Mandelson after further information about “pretty awful emails” between him and Jeffrey Epstein came to light, a minister has said.

Skills minister Baroness Jacqui Smith told Sky News: “When the Prime Minister realised from the additional information provided about the pretty awful emails between Peter Mandelson and Epstein, when the full details of those became available to the Prime Minister last Wednesday afternoon, he very quickly made the decision to remove Peter Mandelson as our ambassador.”

She also told the programme: “Let’s be clear in hindsight, knowing the information that we know now, clearly Peter Mandelson wouldn’t have been selected to be our ambassador.”

She said Sir Keir asked the Foreign Secretary to remove Lord Mandelson from his position.

A minister declined to confirm how many small boat migrants would be sent back to France this week under the “one in, one out” deal as the first flights are expected today.

Skills minister Baroness Jacqui Smith told Sky News: “We’re not going to be talking about specific numbers or specific timing.”

After being repeatedly pressed, she added: “At some point in the future, it will be possible to see the impact that this is having on the overall numbers of people who are coming here and the increased numbers of people who have already been returned because they don’t have a right to be in this country.”

A Labour MP said Sir Keir Starmer will be “gone next May” unless he elects to “change course immediately”.

Richard Burgon, who is on the Left of the party, told BBC Radio 4’s Today Programme: “Lots of MPs are looking to the elections next May, the opinion polls suggest it’s going to be a complete disaster unfortunately.

“I think it’s inevitable that if May’s elections go as people predict, and the opinion polls predict, then I think Starmer will be gone at that time.

“It feels like we are years and years into an unpopular government, rather than a year into a government that’s just got rid of the Conservatives. We’re losing votes to the left, we’re going to be losing seats to the right.

“We face a real threat for the first time in our country’s history of what I would consider to be a far-right extremist government – it’s the Prime Minister’s duty to stop that happening. You can only do that by delivering for people who want real change, and if you can’t do that, then of course, there’s going to have to be change at the very top.”

The MP for Leeds East added: “The Prime Minister needs to change course immediately, otherwise, I’m pretty certain he’ll be gone next May as it stands.”

A minister denied Sir Keir Starmer was in a “last-chance saloon” amid the fallout from the sacking of Lord Mandelson and frustrations from MPs.

Skills minister Baroness Jacqui Smith said the Prime Minister would be meeting with representatives from the nuclear industry in Downing Street to talk about the new deal the UK is striking with the US this week.

Asked whether he was in a last-chance saloon, she told Times Radio: “No, what Keir Starmer is doing today is he’s in Downing Street meeting with representatives from the nuclear industry to talk about the deal we are striking with the US this week to help us to get back control of our energy supply and build more nuclear power.”

The first deportations of migrants under the “one in, one out” deal with France are expected to take place this week.

The first are due to be sent back on a commercial Air France flight on Monday, barring any last-minute legal challenges, The Times reported.