Sugar was appointed "enterprise tsar" by the Prime Minister at the weekend.
The new role immediately prompted accusations from the Conservative Party, claiming the role broke rules on BBC impartiality.
In response, Sugar, who is also to become a Labour lord, denied the position would be a "political thing".
However while speaking at yesterday's event to back apprenticeships, Sugar spoke in front of a giant screen featuring an image of himself and Ed Balls, secretary for schools, children and families.
To avoid commercial conflict Sugar has handed day to day control of his companies to Claude Littner -- who featured in the interview stages of 'The Apprentice'. But BBC editorial chief David Jordan said the broadcaster was still in talks with Sugar over whether there was a conflict.
Jordan said BBC impartiality was "sacrosanct" but added the rules applying to entertainment shows were different to those applying to government news and current affairs.
The BBC's claims regarding the talks have been contradicted by a report in The Sun.
The paper said BBC director general Mark Thompson and BBC director of vision Jana Bennett had already given Sugar the green light two days before the appointment had been officially announced.
Shadow culture, media and sport secretary Jeremy Hunt initially made the complaint over whether Sugar had broken BBC rules in a letter to BBC Trust chairman Sir Michael Lyons.
Following yesterday's presentation in Gateshead, Hunt continued to maintain Sugar was breaking BBC rules.
Hunt said: "Not only has he been using 'The Apprentice' format to draw attention to government policy, he has been promoting and endorsing that policy standing in front of a giant picture of Ed Balls."
Sugar has never made any secret of his allegiance to the Labour party and was reportedly asked about becoming a mayoral candidate to challenge Boris Johnson at the next election.
He has also spoken at Labour fundraising rallies.
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