Labour leader says 'it beggars belief' culture secretary is still in post as email lays bare cosy relationship with News Corp

Labour leader Ed Miliband has ratcheted up the pressure on the culture secretary, Jeremy Hunt, to resign following the disclosure of an email that appears to show he sought "private advice" from News Corporation over how Downing Street should respond to the phone-hacking scandal.

Miliband said "it beggars belief" that Hunt remained in his job and that the "accumulation of evidence" about his links with Rupert Murdoch's company when he was considering its bid for BSkyB made his position untenable.

The email, disclosed to the Leveson inquiry into phone hacking and journalistic ethics by the former News International chief executive Rebekah Brooks, suggests Hunt sought to avoid a public inquiry into phone hacking, suggesting he wanted the firm to "guide his and No 10's positioning" on the scandal.

News Corporation lobbyist Frédéric Michel wrote the email in June 2011, telling Brooks that Hunt was poised to make an "extremely helpful" statement about the company's proposed acquisition of BSkyB, saying the takeover would be approved regardless of phone-hacking allegations.

Miliband said: "One of the reasons so many people hate politics so much right now is that they think politicians stand up for the wrong people, not the right people.

"This is a clear example of that - Jeremy Hunt was standing up for Rupert Murdoch, not for the public interest. Out of touch with the many. Too close to the few. Jeremy Hunt should go."

Labour's deputy leader, Harriet Harman, accused Hunt of colluding with News Corp, saying he was "not fit" to remain in his position. "This is absolutely not acceptable," said Harman. "How much more evidence does David Cameron need that this man is not fit to hold this high office?"

"Clearly there was complete collusion between the secretary of state and his office and News Corp on a bid where he was supposed to be impartial, which is why he should not be in his job.

"Either he didn't know what was going on on an £8bn bid, in which case he shouldn't be in his job and he should be sacked, or he did know and he is covering up and blaming everybody else, in which case he should be sacked."

Labour MP Tom Watson, a leading critic of the Murdoch empire and member of the Commons culture select committee, said that if Hunt "had any decency" he would resign.

"In my view this leaves me completely convinced that he was collaborating not just with News International over BSkyB but also over phone hacking. It's not right, the public know it's not right and David Cameron should act now.

"It shows with absolute clarity what was going on – the government was collaborating with News International."

Labour MP Paul Flynn, a member of the public administration select committee, said that Hunt had clearly "dumped on" his former special advisor Adam Smith and promised the issue would be considered by the committee.

"Hunt's defence is completely implausible," Flynn said. "He's got to go now. This is the worst case of a special adviser being dumped on. Jeremy Hunt is up to his neck in it.

"A resignation delayed is a disgrace multiplied," Flynn added.

A spokeswoman for Hunt insisted that Michel's only contacts were with his special adviser, Adam Smith, who has already resigned after admitting his relations with News Corporation were too close. Hunt acted with integrity throughout and will "vindicate" his position when he gives his evidence to the inquiry, according to the spokeswoman.

The email from Michel to Brooks, dated 27 June 2011, predicted accurately that later that week Hunt would play down the impact of the phone-hacking scandal on the BSkyB bid.

Michel warned her, days before the Guardian revealed that murdered teenager Milly Dowler's voicemail had been targeted by the News of the World, that "JH [Hunt] is now starting to look to phone-hacking practices more thoroughly" and he "has asked me to advise him privately in the coming weeks and guide his and No 10's positioning".

The email showed that Brooks had been told Hunt would approve the long-delayed takeover because he believed "phone hacking has nothing to do with the media plurality issues". Michel told Brooks the sought-after approval would happen later, in the last week of June 2011.

The email stated that Hunt wanted to "prevent a public inquiry"– instead suggesting that parliament's joint committee on privacy and injunctions could carry out a wider investigation.

Michel wrote: "This is based on his belief that the police is pursuing things thoroughly and phone hacking has nothing to do with the media plurality issues. It's extremely helpful."

The accuracy of Michel's predictions in his email was borne out in Hunt's statement to parliament on 30 June, essentially approving News Corp's bid for Sky. Hunt told MPs that "while the phone-hacking allegations are very serious they were not material to my consideration". The News Corp bid was only derailed the following month following the public outcry after the Milly Dowler hacking revelation and the closure of the News of the World.