The Culture Secretary, Jeremy Hunt, was battling to save his political career last night after it was revealed that his office was secretly passing information to the Murdochs during their £7.5 billion bid to take over BSkyB.

Mr Hunt faced demands for his resignation after hundreds of pages of explosive emails, released by News Corp to the Leveson Inquiry, showed that his political advisers engaged in intimate and frequent briefing of the Murdochs’ chief lobbyist to help get the deal through – despite Mr Hunt’s claim to have acted impartially in his exercise of quasi-judicial powers.

One email quoted Mr Hunt saying “we’d get there in the end” and that he “shared” News Corp’s objective of taking over the broadcaster.

Another email, sent by News Corp’s lobbyist the day before Mr Hunt made a statement to Parliament on the bid, drew gasps when it was read out at the Leveson Inquiry: “Managed to get some infos on the plans for tomorrow (although absolutely illegal...!)”

In a day of dramatic revelations at the judicial inquiry, where James Murdoch gave evidence under oath, it also emerged that:

* Mr Murdoch did discuss News Corp’s bid for BSkyB with the Prime Minister David Cameron over Christmas dinner at the Oxfordshire home of Rebekah Brooks – contradicting Downing Street’s previous denials.

* Emails sent by James Murdoch’s lobbyist Fréd Michel show that Mr Hunt’s office would regularly update News Corp on the progress of its bid and how to get it past the regulators – sometimes speaking several times a day, and once even delaying the Culture Secretary’s trip to the ballet.

* The Scottish First Minister, Alex Salmond, showed enthusiasm in supporting the bid. The emails suggest he linked his backing with a request to Murdoch to “smooth the way” for The Sun newspaper to support the Scottish Nationalists.

* News Corp personally threatened Mr Hunt that it would withdraw the bid if he did not hurry things along. “JH repeated he was definitely keen to see this through as quickly as possible.”

The emails directly contradicted assurances that Mr Hunt had given the House of Commons that he was acting as an independent adjudicator of the bid in a quasi-judicial role, Labour said.

The Labour leader Ed Miliband and his deputy Harriet Harman called on Mr Hunt to resign.

The Prime Minister will also now face awkward questioning at the Leveson Inquiry over his discussions with James Murdoch about the BSkyB bid during a Christmas dinner at the home of Rebekah Brooks in December 2010, after James Murdoch contradicted the claim of Mr Cameron’s official spokesman that “he [Cameron] has not been involved in any of the discussions regarding BSkyB, he has been absolutely clear on that”.

The emails also shed light on the extensive and unsuccessful efforts the company undertook to lobby the Business Secretary Dr Cable to approve the deal, before he was stripped of responsibility.

In one email, Mr Michel, News Corp’s director of public affairs in Europe, suggest using the Editor of The Times, owned by News International, to get to see Mr Cable after he had refused to meet with the company. “We should try a very soft approach with him; get him to meet with James Harding... It would be a much better setting than a direct lobbying conversation.”

The memos also reveal that Rupert Harrison, George Osborne's special adviser, was contacted for discussions about what Dr Cable's thinking might be. Harrison admitted there was a good deal of Coalition tension around the issue, and said he would stay in touch.

Mr Hunt told the Commons in June 2011 that: “I am deciding this deal on a quasi-judicial basis, but I have not met Rupert Murdoch or James Murdoch in recent weeks, and all the meetings I have had with them have been minuted and done through official channels.”

Mr Miliband said the disclosures made Mr Hunt’s position untenable: “Jeremy Hunt should have been standing up for the interests of the British people. In fact it now turns out he was standing up for the interests of the Murdochs. He should resign.”

Last night Downing Street said Mr Cameron supported Mr Hunt but pointedly did not express confidence in the process followed by the Department of Culture in deciding the bid. Mr Cameron is likely to face questions on the emails today at Prime Minister’s Questions.

The release of the emails and Mr Murdoch’s evidence also raises questions over the extent to which News Corp is now conducting a “scorched earth” policy over the continued controversy.

James Murdoch and his father Rupert are known to be furious at what they believe to be their “unfair” treatment at the hands of Government ministers and feel they have nothing to lose by shielding them. Rupert Murdoch gives evidence to Leveson today.

In a statement last night Mr Hunt said he had to bring forward his evidence to the Leveson Inquiry to clear his name. "Now is not a time for kneejerk reactions,” he said. “We've heard one side of the story today but some of the evidence reported meetings and conversations that simply didn't happen.

"Rather than jump on political bandwagons, we need to hear what Lord Justice Leveson thinks after he's heard all the evidence.

"Let me be clear my number one priority was to give the public confidence in the integrity of the process. I asked for advice from independent regulators - which I didn't have to do - and I followed that advice to the letter.

"I would like to resolve this issue as soon as possible which is why I have today written to Lord Justice Leveson asking if my appearance can be brought forward. I am very confident that when I present my evidence the public will see that I conducted this process with scrupulous fairness."

The killer emails: Key passages from the News Corp cache

15 June 2010: Take-over announced

The day the starting pistol is publicly fired on News Corp's bid to buy the remaining shares it does not own in BSkyB, the company's public affairs director, Frédéric Michel, emails a senior colleague to tell him that a conversation between James Murdoch (JRM) and Vince Cable, in which the business secretary had supposedly been positive about the proposal, should have been recorded.

"Vince Cable call went very well. He did say he thought "there would not be policy issue in this case". We should have recorded him!"

On the same day, Michel tells Murdoch that Adam Smith, the special adviser to culture secretary Jeremy Hunt, said the Government expects to support the deal.

"Had a call from Hunt's adviser. Said there shouldn't be media plurality issue and believed the UK Government would be supportive throughout the process."

12 October 2010: Editor of The Times

In an apparent reference to News Corps readiness to use its journalists to lobby Cable, Michel emails News International chief executive Rebekah Brooks to suggest James Harding, The Times editor.

"It was suggested that we should try a very soft approach with [Cable]; get him meet with James Harding to get his views on some of BIS key items, like migration cap and get me [FM] to pop... to give him an update on the current battle we face and inform his views. It would be a much better setting than a direct lobbying conversation. Do we think it's ok?"

1 November 2010: Lobbying by friends

Michel tells Murdoch that an unnamed Liberal Democrat MP has agreed to lobby Cable and that SNP leader Alex Salmond is keen to lobby on News Corp's behalf.

"Mission accomplished. Libdem MP, former Sky employee, with major Sky customer centres in his constituency will contact Vince Cable to ask him to bear in mind the economic/investment point of view rather than getting influenced by political games... Alex Salmond is keen to also put the issues across to Cable and have a call with you."

15 November 2010: Call on the mobile

As storm clouds gather over the deal because of growing opposition from other media groups and politicians, Michel tells Murdoch that Hunt is keen to keep channels open.

"Jeremy tried to call you. He has received... legal advice not to meet us today as the current process is treated as a judicial one (not a policy one) and any meeting could be referred to and jeopardise the entire process. Jeremy is very frustrated about it... My advice would be not to meet him today as it would be counter-productive for everyone, but you could have a chat with him on his mobile which is... fine, and I will liaise with his team privately."

Shortly afterwards, Murdoch replies:

"You must be f****** joking. I will text him and find a time."

23 November 2010: Hunt: "Send me the documents privately"

Following the decision by Cable to refer the deal to the media regulator Ofcom, Michel reaffirms the back channel he has opened with Hunt.

"I will have a session with Hunt's adviser next Wednesday to update on Ofcom process and next steps. Jeremy has also asked me to send him relevant documents privately."

14 December 2010: Support voiced

The announcement by Ofcom of the "issues" it will seek answers to from News Corp before reaching a decision on the BSkyB proposal is matched by reassurances from inside the Cabinet.

"Very good debrief with Hunt on the issues letter. He is... amazed by its findings, methodology and clear bias. he... shares our views on it."

In a further expression of support via unofficial channels, Brooks emails Michel to make clear the views of Chancellor George Osborne.

"Same from GO – total bafflement at response."

24 December 2010: Stay in touch

Following the revelation by the Daily Telegraph that Cable has "declared war" on Rupert Murdoch, the business secretary is removed from deciding the BSkyB bid and responsibility passes to Hunt. Contact between Hunt and his office and Murdoch and News Corp might be expected to end. It does not.

From Michel to Murdoch: "Just spoke to JH. Said he was very happy for me to be the point of contact with him/Adam [Smith] on behalf of JRM going forward. Very important to avoid giving the 'anti' any opportunity to attack the fairness of the process and fine to liaise at that political level."

23 January 2011: "Game over"

An increasingly confident News Corp senses victory after Hunt signals to Michel his support for "UILs" or undertakings in lieu to seal the BSkyB deal.

"[Hunt's] view is that once he announces publicly he has a strong UIL, it's almost game over for the opposition... He very specifically said he was keen to get to the same outcome and wanted JRM to understand he needs to build some political cover on the process."

24 January 2011: "Absolutely illegal"

Michel boasts to Murdoch he has received prior notification of an announcement by Hunt about the handling of BSkyB deal.

"Managed to get some infos on the plans for tomorrow [although absolutely illegal...>!]

9 February 2011: Swan Lake

In an apparent sign that News Corp is able to reach Hunt and his office any time, Michel tells Murdoch he's reached them at the ballet.

"I managed to get JH before ... Swan Lake... and have further chat... I told him he had to stand for something ultimately and this was his chance, to dismiss Ofcom's views and show he had some backbone."

2 March 2011 Salmond support

The SNP leader, who is said to be keen to secure the support of The Sun, is reported by Michel to be happy to participate in the BSkyB debate.

"Alex Salmond called. He had a very good dinner with the editor of The Sun in Scotland yesterday. The Sun is now keen to back the SNP at the election. The editor will make his pitch... tomorrow. Alex wanted to see whether we could help smooth the way for the process... On the Sky bid, he will... support the debate"

7 June 2011: Take That

With the deal still mostly on track, News Corp seem in the mood for relaxation. Michel makes it clear he has invited Hunt and his special adviser Adam Smith to a Take That concert.

"I tend to think that [DCMS minister Ed Vaizey] could see us on very specific policy items. We're still involved in the media agenda even during the Sky deal. It's a very punitive decision... By the way, does that mean you and Jeremy will not be coming to Take That on 4th July."

30 June 2011: "Idiotic debates"

Frédéric updates Murdoch on the atmosphere in Hunt's office.

"Had a debrief with JH and his team... He is very happy with the way today went and especially with the absolutely idiotic debates led by [Labour MP] Tom Watson and [John] Prescott."

7 July 2011: Dowler story and 'Leveson'

Following the revelation by The Guardian that the News of the World hacked the phone of Milly Dowler, leading its closure, Michel insists Hunt and his team see no reason to change their stance on BSkyB.

"Spoke to JH. V important to keep same briefing lines as discussed and insist on the plurality issue."

Later the same day, Murdoch is given a flavour of the thinking inside Downing Street about a possible public inquiry into press standards. In a strange development, the closure of the NOTW is floated as a reason to push through the BSkyB deal because the Murdoch's media dominance has been weakened.