The Work and Pensions Secretary and Secretary of State for Wales said he had taken the move to "clear my name" after the Electoral Commission, investigating whether he had broken electoral law, referred the matter to police before lunchtime.

Mr Hain telephoned Prime Minister Gordon Brown at 11.30am after being informed by the Electoral Commission that it was referring the case to the Metropolitan Police.

It is understood Mr Hain offered his resignation at that point "without hesitation" and it was swiftly accepted by Mr Brown.

Minutes later the commission publicly announced it was referring the case involving his campaign cash to the police. Mr Hain confirmed his resignation in a statement.

Mr Hain said: "In view of the Electoral Commission decision today, I will be resigning to clear my name and I will be making a statement shortly."

Downing Street said: "Peter Hain has made his statement. The Prime Minister has accepted Peter Hain's resignation. There will be an exchange of letters in due course."

The Electoral Commission said: "On November 29, 2007, Peter Hain MP informed the Electoral Commission that he had not fully reported to the commission donations he had received for his Labour Party deputy leadership campaign.

"Mr Hain has since met with the commission and provided additional information about donations he received. The Electoral Commission has undertaken a thorough review of this information.

"Following discussions with the Metropolitan Police Service and the Crown Prosecution Service, the Electoral Commission has now referred matters to the Metropolitan Police for them to consider whether an investigation should commence."

The Met confirmed it had launched an investigation.

"We can confirm that the Met has today received a formal referral from the Electoral Commission in connection with potential offences under the Political Parties and Referendums Act 2000 regarding donations received," a spokeswoman said.

"An investigation will now begin by detectives from the Specialist and Economic Crime Command."

Mr Hain quit amid news of the latest police investigation involving Labour and donations.

Police are already probing proxy donations to Labour of more than £600,000 from north east property developer David Abrahams, which Mr Brown has said were "unlawful" and not properly declared.

That case has already claimed the resignation of Labour's general secretary, Peter Watts.

Mr Brown had fought to keep Mr Hain, declaring him to be a "great" minister doing a "good job" on welfare reform.

But as the affair dragged on, support ebbed away.

Confirmation of the police probe was the final straw.

Shadow work secretary Chris Grayling said: "Peter Hain's resignation was inevitable and the right thing to do."