JEREMY Hunt, the culture secretary, was facing calls for his resignation last night, after a trove of emails unveiled at the Leveson inquiry suggested that he was in secret contact with News Corp during its ill-fated bid to buy BSkyB last year.

Hundreds of pages of emails appear to show that the US media giant was regularly discussing its bid to take control of BSkyB with the culture secretary and his advisers, even though Hunt was meant to be acting with quasi-judicial independence in deciding whether to approve the takeover.

The emails from News Corp’s then-head of public affairs Frederic Michel to James Murdoch suggest that Hunt and his advisers passed confidential information about the government’s thinking to the media giant, including some details that could be deemed price sensitive.

Ed Miliband last night accused Hunt of “acting as a backchannel for the Murdochs” and “providing advice, guidance and privileged access to News Corporation”.

The Labour leader insisted that Hunt could not stay in his post and urged the Prime Minister to fire the culture secretary if he refused to resign.

But Hunt said he is confident that he conducted the process with “scrupulous fairness”.

The cabinet minister said in a statement: “Now is the not the time for kneejerk reactions. We’ve heard one side of the story today but some of the evidence reported meetings and conversation that simply didn’t happen.”

Hunt added that he had requested to have his appearance at the media ethics inquiry brought forward to resolve the issue as soon as possible.

The emails were unveiled during Murdoch’s appearance before Leveson yesterday, after which BSkyB’s share price fell by one per cent.

One note from Michel to Murdoch, sent the day before Hunt was to give a statement to Parliament about the News Corp bid, said: “Managed to get some info on the plans for tomorrow (although absolutely illegal..>!)”

But Murdoch told the inquiry that he believed the comment to be a joke due to Michel’s use of punctuation.

Hunt assumed ministerial responsibility for News Corp’s BSkyB bid after Vince Cable was deemed not to be impartial in the matter, having been recorded by undercover reporters saying he had declared war on Murdoch.

During his evidence at the inquiry into media ethics, Murdoch claimed that David Cameron discussed the bid with him over a Christmas lunch hosted by former News International chief Rebekah Brooks in 2010, bringing the PM’s involvement into focus.

James Murdoch’s father Rupert is appearing before Leveson today.