Sir Alan Sugar is prepared to take The Apprentice to another broadcaster if a deal cannot be reached with the BBC that will allow him to be both government adviser and television presenter, The Times understands.

The tycoon, whose peerage is set to be confirmed next week, is still locked in talks with the BBC as to how to reconcile his role as Gordon Brown’s enterprise adviser with his position on the business show.

An exclusive Populus poll for The Times shows that the public is evenly split on the matter, with 43 per cent saying that he should be allowed to combine the positions, while 45 per cent disagree.

Both Sir Alan and the BBC are desperate to agree a compromise that will overcome a fierce attack from the Conservatives alleging that juggling both positions would bring the corporation’s impartiality into question.

Sir Alan wants to sit as a Labour peer but is willing to confirm that he will act in a purely advisory capacity and will not get involved in policy formation or party politics.

He is also thought to have accepted that the programme, the next series of which is expected to run between March and June, would not be screened during a general election campaign, which must be held before June 3.

The BBC, however, is anxious to be seen to uphold the highest standards of impartiality. In a letter earlier this week to Jeremy Hunt, the Shadow Culture Secretary, Mark Thompson, the Director-General, wrote that Sir Alan’s BBC role meant he “should not accept a position in which it is his duty to promote or endorse government policy”.

Sources on both sides say that the Government announced Sir Alan’s appointment before the exact terms of his position had been established, leading to the current impasse.

The programme is made by the independent producer TalkbackThames, which holds the British rights to the format. Such is the current confusion that the programme could go to one of the BBC’s commercial rivals.

“The Apprentice will happen whatever happens with this,” said one source close to the show. “It’s not a BBC production. If it doesn’t happen with the BBC it can move to another broadcaster.”

The corporation will not release details of its contract with TalkbackThames, but it is thought to run on a year-to-year basis. There are understood to be numerous break clauses should the show not meet the BBC’s editorial guidelines.

Because it is publicly funded, the BBC is regulated on impartiality matters by the BBC Trust. But its commercial rivals are governed by regulations overseen by Ofcom, the broadcasting watchdog, which are not as rigorous.

Nothing in Ofcom’s broadcasting code prevents a politician in Sir Alan’s position from fronting an entertainment programme, providing that any coverage of government policy is impartial and balanced. TalkbackThames already sells programmes such as The X Factor and Britain’s Got Talent to ITV, which would jump at the chance to snatch The Apprentice.

A BBC spokesman said: “It is ridiculous to suggest that The Apprentice is moving to another channel.”

The Populus poll, undertaken on Tuesday and Wednesday, shows that Sir Alan divides the nation sharply. The young and the middle classes approve of him, while the middle-aged, elderly and the working classes are more hostile. Nearly half the public approves of Sir Alan’s appointment as the Government’s enterprise champion, with a third disapproving.

However, nearly half the public (49 per cent) believe Sir Alan should not be given a peerage, with fewer than two fifths (36 per cent) thinking he should go to the House of Lords. More than a half among those aged up to 34 support him going to the Lords, but only 17 per cent among those aged over 65. Regarding combining the roles, a half of 18 to 24-year-olds back this, but only a third of those aged over 65, with an even split among the middle-aged.

Populus interviewed a random sample of 1,001 adults aged over 18 between June 9 and 10. For more details, see www.populus.co.uk.

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