Former prime minister Gordon Brown said the situation facing Keir Starmer was "serious" and suggested the Labour leader had been "too slow to do the right things" to clean up politics in the wake of the Peter Mandelson row.
However, Mr Brown backed Mr Starmer as a "man of integrity" who had been "betrayed" by Mr Mandelson.
The Metropolitan Police said its investigation into Mr Mandelson over alleged misconduct in public office would "take some time" after officers finished searching his homes in London and Wiltshire.
Metropolitan Police Deputy Assistant Commissioner Hayley Sewart said: "I can confirm that officers from the Met's central specialist crime team have carried out searches at two addresses, one in the Wiltshire area, and another in the Camden area.
"The searches were related to an ongoing investigation into misconduct in public office offences, involving a 72-year-old man.
"He has not been arrested and inquiries are ongoing."
"This will be a complex investigation requiring a significant amount of further evidence gathering and analysis.
"It will take some time to do this work comprehensively and we will not be providing a running commentary," Ms Sewart said.
Scotland Yard launched its investigation following allegations that Mr Mandelson sent market-sensitive information to the paedophile financier while he was business secretary in Mr Brown’s government during the financial crisis.
Mr Brown said he regretted giving Mr Mandelson his peerage and bringing him back into the government in 2008, adding that he felt "shocked, sad, angry betrayed, let down" when he saw the Epstein messages released by the US Department of Justice.
Read more: Starmer's predictable scandal over Mandelson appointment
Mr Starmer's position is in jeopardy because of his decision to appoint Mr Mandelson as ambassador to the US despite knowing his friendship with disgraced financier Epstein continued after his conviction for soliciting a minor for prostitution in 2008.
Asked what his message was to the Labour Party about Mr Starmer's future, Mr Brown told BBC Radio 4’s Today programme: "This is obviously serious.
"I mean, there’s always speculation. It happened to me, it happened to Tony Blair.
"It happens to everybody about how their future should be gauged.
"But this is serious, and the task is very clear.
"The task is we’ve got to clean up the system, a total clean-up of the system, an end to the corruption and unethical behaviour.
"And if we don’t do it, we’ll pay a heavy price."
He must do the right things now, says Brown
Asked if Mr Starmer was the right man to take the country forward, he said: "I can look in his eyes and I can see that he is a man of integrity. He wants to do the right things.
"Perhaps he’s been too slow to do the right things, but he must do the right things now, and let’s judge what he does, on what happens in the next few months when he tries to, and I believe (he) will try, to clean up the system."
He suggested there should be US-style confirmation hearings for new government ministers and senior appointments.
He said the alleged lies told by Mr Mandelson during his appointment process as US ambassador were "not sufficient explanation for what happened".
"There is a systemic failure to do proper vetting, to go through the proper procedures and to actually have, in my view, what should be public hearings for anybody who is going to be in a senior position representing the British government."
A government spokesman said action was already being taken to clean up Westminster: "Most people who enter public life do so with a strong sense of duty and to make a difference to people’s lives.
"But the shameful and disgraceful behaviour revealed this week is wholly incompatible with public service, and it is right that no one is above accountability.
"We have already strengthened the ministerial code, giving the independent adviser greater powers to launch investigations, introduced a new monthly register of gifts and hospitality, established a new ethics commission, and ensured that ministers who break the rules cannot receive severance payments.
"But Gordon Brown is right that further action is needed in light of what has emerged this week – and we have already begun urgent work on how we can do more."
