Peter Mandelson has resigned from the House of Lords after a series of scandalous emails came to light that linked him to the child sex offender and financier Jeffrey Epstein, including ones that apparently leaked confidential UK government communications.

The move came as Keir Starmer said he had handed a dossier to the police after it emerged Mandelson had sent a string of emails to Epstein containing briefings he received as business secretary under Gordon Brown, including action the government was taking to deal with the global financial crisis.

Starmer told a meeting of the cabinet on Tuesday morning he was appalled by the reported leaks and had also asked officials to draft legislation to strip Mandelson of his peerage “as quickly as possible”.

Mandelson’s departure was announced by the speaker of the House of Lords, meaning he will no longer be a member of the house from Wednesday, though he will retain his title, which can only be removed by an act of parliament.

The prime minister told the cabinet he found it incomprehensible that more could not be done to strip peers of their titles for poor behaviour. “The prime minister believes there is a broader need for the House of Lords to be able to remove transgressors more quickly,” his spokesperson said.

“The prime minister regards it as ridiculous that a peerage cannot be removed except with primary legislation, something that has not happened since 1917. He thinks that in no other walk of life are you unsackable unless a law is passed. He thinks that the country expects the process for removing lords to be fit for purpose, and in line with expectations.”

Addressing the cabinet, Starmer said Mandelson had “let his country down” and added: “For the public to see politicians saying they can’t recall receiving significant sums of money or not was just gobsmacking, causing them to lose faith in all politicians and weaken trust still further.”

The cabinet secretary, the UK’s top civil servant, is investigating the leaked emails sent by Mandelson during the last year of Brown’s government, including ones regarding the potential sale of government assets and an early confirmation of a €500bn European bailout.

Documents have now been passed to the Metropolitan police, who have said they will look at the emails and consider a wider investigation.

Emails forwarded to Epstein from the very top of the UK government while he was business secretary include a confidential UK government document intended for the prime minister outlining a potential £20bn in asset sales.

They also include Mandelson claiming he was “trying hard” to change government policy on bankers’ bonuses, early confirmation of an imminent bailout package for the euro and a suggestion that the JP Morgan boss “mildly threaten” the chancellor over bonuses.

Starmer’s spokesperson said the Cabinet Office was reviewing all information it had about the documents but an initial review of the Epstein files released on Friday by the US Department of Justice found “they contain likely market sensitive information surrounding the 2008 financial crash and the official activities thereafter to stabilise the economy”.

The prime minister is said to have told his cabinet he believed there may be more scandals yet to be uncovered within the cache of emails, saying he was “not reassured that the totality of the information had yet emerged”.

Documents released in the justice department disclosures also appear to show that Epstein paid $75,000 into bank accounts of which Mandelson – then a Labour MP – was believed to be a beneficiary.

Epstein sent Mandelson’s partner, now his husband, Reinaldo Avila da Silva, £10,000 in September 2009 to fund an osteopathy course and other expenses.

MPs told the Guardian they wanted to force further disclosures from Downing Street – including the prime minister’s chief of staff, Morgan McSweeney – about what Mandelson had been asked about before his appointment as US ambassador.

The UK health secretary, Wes Streeting, said that Mandelson’s association with Epstein was a “betrayal on so many levels” but said he could not see how the Cabinet Office or Starmer would have known about the leaking of confidential information to Epstein.

“I can’t see how it would have been known or could have been known, the full extent of Mandelson’s relationship with Epstein or indeed the fact that he was passing sensitive and market-sensitive information to this man whilst as a serving government minister,” he told BBC Radio 5Live.

“I don’t think that could have be known and should have be known. And if anyone is in any doubt about the judgment and integrity of this prime minister, they can judge him by his actions, making sure the ambassador was woken up in the middle of the night and was put on a plane back to London and recalled as our ambassador.”