After Hunt's bruising day of evidence at the Leveson Inquiry on Thursday (May 31), the prime minister immediately issued a statement that he had acted 'properly' while considering News Corp's bid for Sky, despite revelations that he was in contact with James Murdoch.
But Harriet Harman, Labour's deputy leader and shadow culture secretary, said that the party would call for a vote in the House of Commons on whether Hunt should be investigated over a potential breach of the ministerial code.
"Jeremy Hunt should never have been given the quasi-judicial role in the first place as he was biased in favour of the bid," she said in a statement yesterday.
"David Cameron knew this to be the case because of the memo Hunt had sent him where he had expressed clear support for the bid.
"David Cameron said he would stand up for high standards but he is sweeping this matter under the carpet."
The ministerial code governs the way secretaries of state behave, but the Leveson Inquiry heard yesterday that Hunt sent a text to James Murdoch, the then chairman of News International and Sky, to congratulate him on the European Commission giving clearance to the Sky bid on competition grounds.
The text, which read "Great and congrats on Brussels, just Ofcom to go!", was sent within hours of Hunt being handed the job of adjudicating over the takeover after it had been stripped from Vince Cable, the business secretary who had been secretly recorded saying he had "declared war" on News Corp boss Rupert Murdoch.
Even after taking on authority for the review process, Hunt maintained the line of contact with James. He received a message from the News Corp executive on March 3, just after publicly saying that he was "minded to approve" the Sky bid, saying: "Big few days. Well played. JRM."
The culture secretary's special adviser, Adam Smith, also resigned last month after revelations about his close contact with News Corp lobbyist Fred Michel during the £8bn Sky bid.
Speaking on BBC Breakfast this morning (June 1), Harman said: "The ministerial code is what is supposed to govern the way secretaries of state behave, and when David Cameron came into power he said it was very important indeed.
"He was going to have higher standards in public office and he upgraded the code. Now he has just torn it up."
At the Leveson Inquiry, Hunt said that he had been "sympathetic" to the takeover as a potentially positive development for UK media, but claimed that his actions during the review process, particularly the involvement of Ofcom, showed that he had not been biased.
The Guardian has written that Hunt is likely to be safe in his post until a late summer reshuffle of the Cabinet, but his authority in the media industry is now "severely damaged".