The former work and pensions secretary was asked to help a property company owned by Pervaiz Naviede, the financier behind DNA Bioscience, the company of which Mr Blunkett was briefly a director.
A spoken letter obtained on audio cassette by The Observer reveals Warren Smith, the chairman of Mr Naviede's Legendary Property Company, giving Mr Blunkett a "wish list" of departments to lobby together with policies the company wished to influence.
The newspaper says Mr Blunkett initially denied taking the matter further but later admitted sending "details" of Mr Smith's letter on to David Miliband, then Minister for Local Government in the Office of the Deputy Prime Minister.
A statement from Mr Blunkett's office released this weekend states: "Mr Blunkett received the tape from Warren Smith in April. The only action taken was that he agreed to meet him for supper. They had supper late on Tuesday 3 May, where Mr Blunkett explained that were he to return to Government there would be nothing he could do to assist."
However, his office later admitted sending details of the letter on to Mr Miliband as "the minister responsible" just a few days after the election.