Officials at No 10 and the Foreign Office were aware of supportive emails between Lord Mandelson and paedophile Jeffrey Epstein when the prime minister initially defended the former ambassador on Wednesday, the BBC understands.

Sources stressed Sir Keir was not aware of the contents of the emails when he stood by Lord Mandelson at Prime Minister’s Questions on Wednesday.

The BBC understands that a media enquiry outlining details of the messages between the pair was sent to the Foreign Office on Tuesday, and passed on to No 10.

Sir Oliver Robbins, permanent under-secretary at the Foreign Office, asked Lord Mandelson about the emails on Tuesday but did not receive a response until the next day.

Conservative leader Kemi Badenoch accused the prime minister of lying to the public.

She said: “Looks like the prime minister and Labour MPs spent the week lying to the whole country about what they knew regarding Mandelson’s involvement with convicted paedophile Jeffrey Epstein.

“If No10 had those emails for 48 hours before acting, it means he lied at PMQs and ministers lied again about new additional information. These are yet more errors of judgement”.

Backbench Labour MP Olivia Blake called No 10’s reported handling of the situation “really embarrassing”.

She told BBC Radio 4’s Today programme on Saturday: “Any operation that fails to tell a prime minister when something as substantial as those emails were presented to them clearly has deep failings.”

Blake added: “Whoever is gatekeeping the information to the prime minister needs to stop, and they need to be getting things to him much earlier so that he can get on top of it.”

Asked whether Lord Mandelson should be required to leave the House of Lords, Blake said it was something “we should be considering”.

Downing Street later said the prime minister “strongly” rejected criticism of the leadership in No 10 from some of his MPs.

Starmer maintained full confidence in his “top team” and was “focused on delivering for the country,” they said.

Downing Street also rejected claims the prime minister is failing to engage with MPs, saying he meets with backbenchers “regularly” and pointing to a meeting held on Monday night, which they say was “positive”.

Badenoch also said the prime minister had “very serious questions to answer”.

“The only way to clear this up is full transparency about who knew what, and when,” she added.

Lord Mandelson was sacked as the UK’s ambassador to the US shortly before 11:00 on Thursday. Downing Street said the emails contained “new information” that was not known at the time of Lord Mandelson’s appointment.

The full emails were published by Bloomberg and the Sun on Wednesday evening.

“I think the world of you and I feel hopeless and furious about what has happened,” Mandelson wrote the day before Epstein reported to prison in 2008 for soliciting sex from a minor.

Mandelson added: “You have to be incredibly resilient, fight for early release… Your friends stay with you and love you.”

In an interview with the Sun on Wednesday, Lord Mandelson said he felt a “tremendous sense of regret” that he had met Epstein, and that he “took at face value the lies that he fed me and many others”.

The BBC earlier reported that Lord Mandelson’s emails were sent from an old account to which he no longer had access. Officials cite this as the reason they had not been seen earlier.

In a statement announcing Lord Mandelson’s dismissal, the Foreign Office said: “The emails show that the depth and extent of Peter Mandelson’s relationship with Jeffrey Epstein is materially different from that known at the time of his appointment.”

Following his sacking, Mandelson said being the UK’s ambassador to the US had been “the privilege of my life”.

It comes as Sir Keir faces growing pressure over his handling of Lord Mandelson’s appointment as ambassador to the US.

Labour MP Clive Lewis, an outspoken voice on the Labour left, said Sir Keir “doesn’t seem up to the job”, adding that there was a “very, very dangerous atmosphere” among Labour MPs.

Another Labour MP Jo White said the “clock is ticking” for Sir Keir to turn polls around before local elections next May.

Labour MP Emily Thornberry, chair of the foreign affairs committee, has written to the new Foreign Secretary Yvette Cooper asking for details on the vetting process for Lord Mandelson’s appointment, and whether security concerns were dismissed.

Thornberry’s letter was first reported by Sky News.

It also emerged that Jeffrey Epstein paid for Lord Mandelson’s travel on two separate occasions in 2003 totalling more than $7,400 (£5,400), according to documents released by the US House of Representatives Oversight Committee.

Earlier this week, US lawmakers released an alleged “birthday book” containing messages sent to Jeffrey Epstein on his 50th birthday in 2003 – including one from Lord Mandelson.

In his letter, which features photos of the pair, Lord Mandelson described Jeffrey Epstein as his “best pal”, and an “intelligent, sharp-witted man”.