The Conservatives have formally complained to the BBC's governing body over the decision that Sir Alan Sugar will continue on The Apprentice.
The corporation said yesterday that Sir Alan's new role as a Government adviser would "not compromise the BBC's impartiality".
Questions had been raised about whether the entrepreneur's new Enterprise Tsar role could breach impartiality rules during the General Election campaign.
The 62-year-old, who will take a seat in the House of Lords following a Cabinet reshuffle earlier this month, said he was "glad" about the decision.
Shadow culture secretary Jeremy Hunt has made a formal complaint about impartiality to the BBC Trust.
In a letter to the Trust's chairman, Sir Michael Lyons, Mr Hunt said: "Rather than set my mind at ease, the justifications for allowing Sir Alan to take up his Government role given by the Director-General actually makes things worse.
"Having therefore now exhausted the complaints procedure with the BBC, I would now like to make a number of official complaints to the BBC Trust about a breach of editorial guidelines."