The Daily Telegraph has gone to war with Downing Street after accusing David Cameron's top spin doctor of threatening the newspaper with the spectre of press regulation if it refused to drop an investigation into the culture secretary's expense claims.

On Wednesday afternoon the newspaper accused Craig Oliver, the Downing Street communications director, of calling its editor Tony Gallagher to suggest he back off the story as “she [Maria Miller] is looking at Leveson at the moment".

The prime minister's spokesman said: "The Secretary of State had some concerns about the way that investigation was conducted. She set those out in a letter to the editor. Craig Oliver was simply reflecting those concerns."

It is highly unusual for a newspaper to publish off the record conversations of this kind between its journalists and ministers or their political advisers.

The Daily Telegraph said it had done so in order to highlight the danger of introducing any form of statutory regulation of the press.

On Wednesday morning the Daily Telegraph claimed that Joanna Hindley, an adviser Maria Miller, had initially attempted to stop a story that accused the culture secretary of misusing £90,000 of expenses, a charge she denies.

Labour MP John Mann has complained to the Parliamentary Commissioner for Standards that Miller’s parents lived in a property designated as her second home whilst she was also claiming parliamentary allowances to cover the costs of the rent.

A spokesperson for the Department of Culture, Media and Sport said: "Mrs Miller’s special adviser raised concerns with a journalist about the nature of an approach to Mrs Miller’s elderly father.

"Her advisor noted Mrs Miller was in regular contact with the paper’s editor and would raise her concerns directly with him.

"However, this is a separate issue to ongoing discussions about press regulation. Mrs Miller has made the government’s position on this clear."

The paper reports that Oliver told Gallagher that Maria Miller was considering complaining to the Press Complaints Commission before reminding him that the culture secretary was leading the government's response to Leveson Report.

In his report on media ethics, Lord Justice Leveson recommended that the government underpin a new independent regulator of the press with legislation, something David Cameron has refused to endorse.