Labour MPs are publicly and privately expressing their anger over the appointment of Peter Mandelson as the UK ambassador to the US and the handling of his subsequent sacking.

Mandelson was dismissed over his links to convicted paedophile Jeffrey Epstein. The men’s friendship had been known about at the time of his appointment but No 10 said new information about their relationship only came to light this week.

One Labour MP described the situation as a “shambles” and a government minister said they were “starting to wonder how sustainable it is” for Morgan McSweeney, the prime minister’s chief of staff, to stay in post.

McSweeney is increasingly being blamed for Lord Mandelson’s appointment.

Several senior Labour figures claimed McSweeney had been resisting the inevitability of Mandelson’s departure on Wednesday, with one insider describing “cold, hard fury” amongst those in Downing Street about the episode.

However, another senior No 10 source claimed this was nonsense, saying that by Wednesday afternoon McSweeney was adamant that Mandelson’s position was untenable.

A Labour MP told the BBC: “Panic has started to set in”, urging the prime minister to “get a grip” and warning that only publishing correspondence between No 10, McSweeney and Lord Mandelson before his appointment as ambassador would “put this to bed”.

Another MP said “It’s quite clear the buck should stop with him [McSweeney].

Asked if Sir Keir Starmer had confidence in McSweeney, the PM’s spokesperson said “the prime minister has confidence in his top team and they are getting on with the important work of this government.”

Some backbench Labour MPs have publicly expressed their anger. Paula Barker said: “The delay in sacking him [Mandelson] has only served to further erode the trust and confidence in our government and politics in the round.”

Her backbench colleague, Charlotte Nichols, said Mandelson’s sacking was “not immediate enough unfortunately, as he should never have been appointed in the first place”.

Speaking to BBC Breakfast, Scottish Secretary Douglas Alexander said: “In retrospect, of course, if [it] had been known at the time what is known now, the appointment wouldn’t have been made.”

He acknowledged Labour MPs will be feeling “despondent” following a chaotic week which has seen the sacking of Lord Mandelson and the resignation of Angela Rayner.

“Many of us were devastated by [deputy PM] Angela Rayner’s departure from the government last week.

“Now to have the dismissal of Peter Mandelson just the next week, I totally get it, of course Labour MPs will be despondent that in two weeks in a row we have seen significant resignations from public service.

“These are not the headlines any of us in government or in Parliament would have chosen or wanted.

“But the fact is when the evidence emerged, action had to be taken and we are looking forward, therefore, to moving on.”

Conservative frontbencher Alex Burghart said his party would force a vote in Parliament to release the documents that the prime minister and the foreign secretary were shown before appointing Lord Mandelson.

“Those documents exist, they will be on file… it’s inconceivable they would not have been shown concerns raised by the security services through the vetting process,” he told BBC Breakfast.

Liberal Democrat foreign affairs spokesperson Calum Miller said that “to avoid further national embarrassment” Mandelson’s successor should take questions from the foreign affairs committee before having their appointment confirmed.

Emily Thornberry, chair of the committee, said she had “repeatedly” asked to question Mandelson ahead of his appointment.

“The Foreign Office should not have stopped us from asking questions. The government should welcome such scrutiny.”

Reform UK Leader Nigel Farage said Lord Mandelson was “an enormously talented bloke” but his appointment “was a serious misjudgement from the prime minister.”

He said it “is about the prime minister’s judgement but also about the role that Morgan McSweeney plays in this government” adding: “I think McSweeney’s role is now considerably in doubt.”

Lord Mandelson’s association with Epstein was publicly known when he was given the Washington job.

However, at the start of the week, US lawmakers published documents from Epstein’s estate including 2003 birthday messages from Mandelson in which he refers to Epstein as “my best pal”.

On Wednesday, Sir Keir said he had confidence in Lord Mandelson and insisted “due process” had been followed in his appointment.

But the following day he decided to sack his ambassador.

It came after a series of emails from Lord Mandelson to Epstein were published by the Sun and Bloomberg.

The emails included supportive messages Mandelson sent after Epstein had pleaded guilt to soliciting prostitution from a minor in June 2008.

In one message, Mandelson is reported to have told Epstein to “fight for early release” and, the day before began his sentence, “I think the world of you.”

The BBC has been told the information published on Wednesday evening was not available to those in government when Lord Mandelson was appointed, as they came from what has been described as a “long closed” email address.

Douglas Alexander said he felt “incredulity and revulsion” when he read the emails, which he said “had not in any way reached the prime minister” during the appointment process.

“When that reached the prime minister’s desk, he acted and dismissed the ambassador.”

He said Lord Mandelson had initially been appointed because the UK needed an “unconventional ambassador” to work with Donald Trump’s “unconventional presidential administration”.

James Roscoe, the deputy head of the Washington embassy, has been appointed as interim ambassador ahead of the US President’s state visit to the UK next week.

Additional reporting by political correspondents Nick Eardley and Georgia Roberts