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 Mr 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 Mr Hunt's office released market-sensitive information to News Corp in breach of City rules.

In a letter 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 on Wednesday 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 Mr 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".

Labour leader Ed Miliband said it was "incredible" that Mr Hunt was still Culture Secretary and accused Mr Cameron of using him as a "firewall".

Jonathan Stephens, the Culture Department's permanent secretary, refused to answer questions about links to the Murdoch empire when he appeared before the Public Accounts Committee on Thursday. The committee relayed the suggestion that he had agreed as a permanent secretary to enable Mr Smith to act as a channel to the Murdoch empire.

Mr Stephens said the department would co-operate with the Leveson Inquiry, adding: "I am very sorry. These are very important matters. They are rightly the subject of interest and that is why the Secretary of State made the statement on the question (yesterday) and that is why he wants to give evidence to the Leveson Inquiry and is preparing his evidence."