The BBC has been accused by a British Cabinet minister of "pursuing an agenda" against Culture Secretary John Whittingdale, after disclosing that he had a six-month relationship with a woman later exposed as a prostitute.

Senior sources said the report was broadcast while discussions over the licence fee are at a crucial stage, with Whittingdale seeking to make the BBC hand public money to other broadcasters for some programming.

Just days after a key discussion on the proposal, the BBC's Newsnight aired allegations about Whittingdale's private life which had been circulating among newspapers for more than two years, but had not been published on the basis that they invaded the divorced minister's privacy.

Downing Street immediately faced calls, including from some Labour figures, for Whittingdale to be demoted or dismissed.

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The BBC strongly denies the accusation that the broadcast was motivated by the licence fee discussions. Executives said it was an editorial decision taken by Newsnight. The disclosure that Whittingdale had a relationship with a woman he met on an online dating site, but later found to be a prostitute, led BBC broadcasts.

However, the minister was backed by Downing Street while other senior Labour politicians said that there was no public interest in the disclosure.

A Cabinet ally of the Culture Secretary told the Daily Telegraph: "The way the BBC has marched into a story that should be an entirely private matter and is hardly in the public interest suggest that they have got an agenda in attacking John. His reputation is being smeared.

"It is really not the way we expect a major public service broadcaster to behave. People will conclude that it's all about the licence fee."