Culture Secretary Jeremy Hunt has insisted he behaved "scrupulously fairly" as he fought for his political life over claims that he secretly backed News Corporation's bid to take over satellite broadcaster BSkyB.

The Tory Cabinet minister told reporters as he left his home that he is going to be making a "very, very determined" effort to show that he acted with "total integrity" in his conduct of the process of deciding whether to approve the deal.

"I made my position very clear, I am going to be making a very, very determined effort to show that I behaved with total integrity and conducted this process scrupulously fairly," he said.

Mr Hunt's remarks come after he requested an early date at the Leveson Inquiry into press standards to give evidence after claims that emails released on Tuesday showed that he acted as a "cheerleader" for the News Corp bid.

Labour leader Ed Miliband called for Mr Hunt to resign, accusing him of "acting as a back-channel" for the Murdochs. The row is set to intensify as Labour prepares to face down David Cameron over the allegations at Prime Minister's Questions.

Mr Cameron's own links to the Murdochs will also come under the spotlight following Tuesday's evidence from James Murdoch at the inquiry. The News Corp executive revealed he and the Prime Minister had briefly discussed the BSkyB bid in December 2010 - two days after Business Secretary Vince Cable was stripped of his decision-making power on the takeover. That was at a Christmas dinner hosted by News International chief executive Rebekah Brooks which the PM attended on December 23, 2010.

Mr Murdoch told the inquiry that he and Mr Cameron mentioned what had happened. "He reiterated what he had said publicly, which is that the behaviour had been unacceptable, and I imagine I expressed the hope that things would be dealt with in a way that was appropriate and judicial," he said. "It was a tiny conversation ahead of a dinner where all these people were there, so it wasn't really a discussion."

The inquiry released a 163-page dossier of emails detailing contacts between the Culture Secretary's office and a senior executive at News Corp. Labour said the documents showed Mr Hunt failed to fulfil his quasi-judicial role in relation to the proposed takeover, which he had promised to carry out in a "fair and even-handed" way.

Former deputy prime minister Lord Prescott told Sky News Mr Hunt should come to the Commons to explain his actions, adding: "I can't understand why Mr Hunt - instead of applying to Leveson, why doesn't he come before the House of Commons and explain there is no truth in these allegations?"

He added: "I hope that today's Prime Minister's Questions, I hope Mr Cameron, who is heavily involved in all this despite his denials, will now actually get him to come to the House of Commons. If he is so clear that he has done his job properly and impartially, come and tell the House of Commons. Why ask Lord Justice Leveson as to whether he would allow him to appear before? It means delay, delay, delay."