David Cameron is under pressure to order an inquiry into claims that culture secretary Jeremy Hunt broke ministerial rules in his dealings with Rupert Murdoch's News Corp empire.

Labour has identified what it said were three specific breaches by Hunt of the ministerial code of conduct in his handling of News Corp's £8 billion takeover bid for broadcaster BSkyB.

Meanwhile the Financial Services Authority was reported to be considering an investigation into whether Hunt's office released market-sensitive information to News Corp in breach of City rules.

Ed Miliband said it was "incredible" that Hunt was still culture secretary and accused Cameron of using him as a "firewall".

He told BBC Radio 4's Today programme: "It beggars belief that he's still in his job, because to believe that he should stay you have to believe that his special adviser was, if you like, a lone wolf, who spent six months in collusion with News Corporation, passing information that was to be announced in the House of Commons, providing information about discussions with the regulator, providing information about what opposing parties were saying.

"I think it's incredible that Jeremy Hunt hasn't resigned and that that David Cameron has kept him in his job."

He added: "Why is Jeremy Hunt still in his job? Because David Cameron has questions to answer, and Jeremy Hunt is, if you like, acting as a firewall, and if he goes the questions will then move to David Cameron's conversations with Rebekah Brooks, with James Murdoch and others."

In a letter last night to the Prime Minister, Labour deputy leader Harriet Harman said he must now refer the case to his independent adviser on ministers' interests, Sir Alex Allan.

The latest storm to rock the Government centres on the release by the Leveson Inquiry into media standards of an explosive 163-page dossier detailing contacts between a News Corp executive, Frederic Michel, and Mr Hunt's office.

Amid noisy scenes in the Commons, Mr Hunt yesterday denied the stream of emails and texts represented a secret "back channel", insisting he had carried out his quasi-judicial role in relation to the News Corp bid with "scrupulous fairness".

However he was forced to accept the resignation of his special adviser Adam Smith, admitting his contacts with Mr Michel had "overstepped the mark" and were "clearly not appropriate" in a such a quasi-judicial process.

Downing Street was clearly hoping Smith's departure would draw a line under the affair, with Mr Cameron insisting that Mr Hunt had "my full support for the excellent job that he does".

However Labour remains determined to keep up the pressure. In her letter, Harman said Hunt had breached the ministerial code by failing to take responsibility for the actions of his special adviser.

She said he had also failed to give "accurate and truthful information" to Parliament when he claimed last year to have published all documents and details of all exchanges between the Department of Culture Media and Sport and News Corp.

And in a third alleged breach of the code, she said advance details of a parliamentary statement had been passed to News Corp before the Commons had been informed.

"These must now be referred to the independent adviser on ministers' interests as a matter of urgency," she said.

A former director general of the Office of Fair Trading said confidence in Britain's "administrative justice" was being damaged.

Asked whether Hunt had strictly followed due process, John Bridgeman told BBC Radio 4's Today programme: "We don't know yet, do we? We are looking for more about it."

But he added: "Private conversations, which tend to be one-sided, tend to be selective with the facts, private conversations with special advisers, are not helpful.

"I don't think it gives the necessary reassurance to institutions, other people who want to come and do business in this country, that we are protecting the integrity of our systems by which these important systems are taken."

Bridgeman said the systems were "being abused".

"Private conversations are allowed to take place when the matter is being properly considered by the authorities.

"If you look at the criminal justice system, if these things happened with judges or a jury, it would be seen as contempt."