Pressure has continued to mount on Jeremy Hunt after Labour revealed it will force a Commons vote calling for the beleaguered Culture Secretary to face an independent investigation into claims he breached the ministerial code.
The Cabinet minister held on to his job after Downing Street said his evidence to the Leveson Inquiry showed he "acted properly" in his handling of the News Corporation bid for BSkyB.
Shadow Culture Secretary Harriet Harman announced that Labour would use its opposition day debate on Wednesday June 13 to demand that an inquiry into Mr Hunt's actions is launched by Sir Alex Allan, the Prime Minister's adviser on the ministerial code.
Senior Conservative Bernard Jenkin also waded into the row by renewing his calls for Sir Alex to be given the power to stage inquiries without the Prime Minister's permission.
The Public Administration Select Committee (PASC) was preparing to "consider the matter again" after recess, he warned.
Labour believes Mr Hunt misled Parliament about his role in the bid for BSkyB and must also take responsibility for the actions of his special adviser Adam Smith who was forced to quit when a slew of damaging emails were released showing close contact with News Corporation lobbyist Fred Michel.
Ms Harman said: "Jeremy Hunt has broken the ministerial code and misled parliament. It is not acceptable that these rules have been broken and we will call a vote insisting that Jeremy Hunt's breaches of the code are referred to the independent adviser on ministerial interests.
"The ministerial code sets the standards which secretaries of state must live up to. When David Cameron came into power, he upgraded the code and he said he was going to have higher standards in public office. Today those words ring hollow, he has just torn up the code."
Michael Fallon, deputy chairman of the Conservative party, insisted nothing new had emerged during Hunt's evidence to the inquiry and claimed Labour "pre-judged this right from the start".
"Ms Harman actually called for him to resign before they had seen his evidence," he told Sky News.
Mr Hunt told the inquiry he considered quitting following the wave of allegations about his handling of the takeover bid.
"I did think about my own position," he said. "But I had conducted the bid scrupulously fairly throughout every stage and I believed it was possible to demonstrate that, and I decided it wasn't appropriate for me to go."
The Culture Secretary accepted that chatty messages he exchanged with James Murdoch while he was responsible for deciding on the BSkyB issue were, with hindsight, inappropriate.
Among messages between the pair was one congratulating the media executive on a promotion to a new News Corp job in New York, in which Mr Hunt joked: "I am sure you will really miss Ofcom in NY!"
Mr Murdoch replied, in an apparent reference to the takeover bid: "Sadly I fear they won't see the back of me that easily! Hopefully we can move our other business forward soon."
Mr Murdoch also sent a text congratulating Mr Hunt after the Culture Secretary's decision in March 2011 that he was minded to support the takeover bid following the media giant's offer to spin off Sky News.
In a text signed with his initials, Mr Murdoch said: "Big few days. Well played. JRM"
Mr Hunt replied: "Thanks think we got right solution!"
The Culture Secretary insisted that such messages "had absolutely no impact on the process" and were "just me being courteous", although he added that he would avoid such contact in similar circumstances in the future.
"I think probably now I would not take the same view and would avoid all text messages," he said.
Downing Street's announcement that Mr Cameron would not refer the matter to Sir Alex came within minutes of the conclusion of Mr Hunt's six-hour evidence session, fuelling Labour claims that the issue was being "swept under the carpet".
In March the PASC published a damning report on the advisory role held by Sir Alex, claiming it "lacks independence in practice" as it is "in the gift" of the PM and cannot instigate investigations.
Meanwhile, Mr Jenkin, the committee's chairman, said: "PASC has previously made clear, both in a recent report and in a report issued during the last parliament, that the Prime Minister's adviser on ministerial interests should not have to depend on a referral from the Prime Minister in order to determine whether or not there has been a breach of the ministerial code.
"It is likely that that PASC will consider this matter again when parliament resumes after the Whitsun recess."
Sir Philip Mawer, the Prime Minister's former adviser on ministerial interests, quit the post shortly after Liam Fox resigned as defence secretary for breaching the ministerial code over his working relationship with his friend Adam Werritty. He has since expressed his "frustration" that Mr Cameron did not call him in to handle the case.