Murdoch-owned newspapers such as The Times, Sun and News of the World have been significantly more zealous than other newspapers in backing No 10 over the BBC.
A source on The Times said yesterday there was "unease" among its journalists about the paper's recent coverage of the dispute.
Responding to a story in The Times, the BBC said it was considering legal action if it did not get an apology from an MP who told the paper that Gavyn Davies, the BBC chairman, had misled governors over the identity of the source for its Iraqi dossier story.
In a letter to the paper yesterday Lord Ryder, the deputy chairman, challenged Robert Jackson's claim and said Mr Davies had not known the source was Dr David Kelly at the time of the meeting.
While, under recent editors, newspapers like the Sun and The Times have rarely been slow to criticise the BBC, the ferocity of the attack intensified this week. Speculation that someone above the level of editor had intervened was fuelled on Saturday when News of the World staff were surprised by a sudden switch in the paper's editorial line over the row.
Journalists had spent the day working on a piece critical of the Government only to be told late in the afternoon they were now to write one that was sympathetic. Sources on the paper claim the turnaround was ordered "straight from the top".