Labour has stepped up demands for Jeremy Hunt to be sacked, amid fresh claims he colluded with Rupert Murdoch's empire in a bid to prevent a public inquiry into phone hacking.

A newly-disclosed email from News Corporation public affairs executive Fred Michel said the embattled Culture Secretary wanted the firm to "guide his and Number 10's positioning" on the scandal.

It also boasted of a tip-off about an "extremely helpful" statement Hunt was due to make to MPs on the BSkyB bid.

Following the disclosure, in material released to the Leveson inquiry by former News International boss Rebekah Brooks, Labour said David Cameron must act to get rid of Hunt.

"This is absolutely not acceptable," said Labour deputy leader Harriet Harman. "How much more evidence does David Cameron need that this man is not fit to hold this high office?"

But 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.

The Culture Secretary 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.

"He will be repeating the same narrative as the one he gave in Parliament few weeks ago," Michel wrote.

"This is based on his belief that the police is pursing things thoroughly and phone hacking has nothing to do with the media plurality issues.

"It's extremely helpful."

The email stated that Mr Hunt wanted to "prevent a public inquiry" - instead suggesting that Parliament's Joint Committee on Privacy and Injunctions could carry out a wider investigation.

"For this the committee will need to come up a strong report in the autumn and put enough pressure on the PCC (Press Complaints Committee) to strength itself and take recommendations forward," Michel wrote.

"JH is now starting to looking to phone hacking/practices more thoroughly and has asked me to advise him privately in the coming weeks and guide his and No 10's positioning."

A month later reports emerged that Milly Dowler's mobile phone had been accessed, sparking a public outcry and leading David Cameron to launch the Leveson Inquiry.

Harman said: "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 £8 billion 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."

But a spokeswoman for Hunt insisted: "Jeremy Hunt will respond to this when he gives evidence to the Leveson Inquiry in due course. He is confident his evidence will vindicate the position that he has behaved with integrity on every issue.

"It has already been made clear that when Fred Michel has claimed in emails to be speaking to Jeremy Hunt that was not the case.

"On July 11 2011 Jeremy Hunt wrote to Ofcom for further advice about the impact of phone hacking on the BSkyB bid."