Scotland Yard's Deputy Assistant Commissioner John Yates made the request at a Westminster meeting.

The police are worried public committee hearings could unwittingly undermine their inquiry.

Mr Yates said he had made significant progress in the ongoing investigation into the alleged scandal.

This is the second time MPs have been asked to delay the parliamentary inquiry into the allegations.

The Public Administration Committee wanted to interview some of the millionaire businessmen who had made loans to the Labour Party as well as Tony Blair's chief fundraiser, Lord Levy.

But in March they agreed to postpone their inquiry at the request of Scotland Yard.

The BBC's Political Editor Nick Robinson said MPs would be concerned about what to do next and he added the prime minister would also be worried.

He said the police have suggested their investigation may not finish until September, which, if correct, "could not be worse" for Mr Blair.

That could mean the investigation is not completed until just before the Labour Party conference, which will be a critical one for Mr Blair, Nick Robinson added.

On Monday evening the MPs met Mr Yates and lawyers from the Crown Prosecution Service.

The MPs are taking legal advice and are expected to make a statement on Tuesday.

Proper aim

In a statement Mr Yates said he recognised the "proper aim" of such inquiries but warned: "We are seeking the continued cooperation of all interested parties that their inquiries do not unwittingly undermine the criminal investigation."

Despite the warning, the MPs later decided to press ahead with plans to question Cabinet Secretary Sir Gus O'Donnell on Tuesday.

They will also quiz Lord Stevenson and Lord Hurd, both from the independent Lords appointments commission which voiced concern about some of the Labour lenders nominated for peerages.

Mr Yates said the police had received a wide range of allegations since their inquiry began.

'Worth investigating'

But the investigation remained focused on whether peerages were offered in exchange for loans to political parties or sponsorship of the government's flagship city academies.

"Significant progress has been made in the inquiry to date, although in many ways the investigation is still at a relatively early stage," said Mr Yates.

"A large amount of documentation has been provided to us and it is a major and ongoing task for the investigation team to examine it all.

"We have already identified a number of issues that merit further detailed examination."

The police have interviewed some people under caution and others as witnesses without caution.

Loans rules

Last month, Des Smith, a head teacher from East London was arrested by detectives under the 1925 Abuse of Honours Act which forbids the sale of peerages.

Mr Smith was the first person to be interviewed under caution as part of the inquiry. He was later released on police bail. Mr Smith has categorically denied the allegations and says he will be contesting them vigorously.

Both the police and the MPs launched their inquiries after it emerged that some people who had been nominated for peerages by Tony Blair had given Labour large loans before last year's election.

The investigation has been widened to include loans to the Conservatives and the Liberal Democrats.

The rules on political funding meant that all large political donations had to be declared - but details of large loans did not have to be published.