Jeremy Hunt appears to have survived his brush with the Leveson inquiry.

The culture secretary went into the hearing amid widespread doubts over his ministerial future. But he emerged with the backing of the prime minister.

Close links between Mr Hunt’s special adviser Adam Smith and Fred Michel, a lobbyist for Rupert Murdoch’s News Corp, led to Mr Smith’s departure from the Department of Culture, Media and Sport earlier this month.

Mr Hunt insists he kept the Murdochs at arm’s length after responsibility for authorising News Corp’s bid to but out the satellite broadcaster BSkyB passed to him from Vince Cable in December 2010.

But only a few hours before he inherited the decision-making powers Mr Hunt was in close contact with James Murdoch. He dodged a bullet today, but has Jeremy Hunt really cleared his name?

Did he break the ministerial code?

Labour say the culture secretary has broken the code of conduct for cabinet ministers in three ways.

They say Mr Hunt misled parliament in March 2011 when he insisted he had published “all the documents relating to…all the exchanges between my department and News Corp”, despite not coming clean about emails and texts until later.

He also allegedly tipped off News Corp about his decision on the BSkyB bid before he told the House of Commons – a big parliamentary no-no – and failed to take full responsibility for Mr Smith’s actions.

Mr Cameron said today there will now not be an inquiry into these allegations by Sir Alex Allen, his adviser on the ministerial code.

That’s a little surprising because at the very least, the flood of emails between Messrs Smith and Michel that have only emerged in the previous weeks suggests there is a case to answer on the first point.

The accusation that Mr Hunt or someone close to him leaked the contents of his statement on the BSKyB bid in January 2011 stems from an email Mr Michel sent to James Murdoch the day before the statement, saying: “Managed to get some infos on the plans for tomorrow (although absolutely illegal!).”

Of course we don’t know how the information was apparently leaked and there’s no evidence of wrongdoing by Mr Hunt on that score.

The question of whether the minister took the appropriate responsibility for the scale of correspondence between his special adviser and Mr Michel is more tenuous, as the ministerial code doesn’t spell out exactly what Mr Hunt is supposed to do if an adviser misbehaves.

Did he mislead Parliament on other occasions?

On April 25 Mr Hunt faced a grilling from fellow MPs but defended his actions robustly.

Labour MP Chris Bryant said today that Mr Hunt’s latest evidence to Leveson contradicts what he told parliament last month.

Mr Hunt told MPs: “What was not right was for me to be involved in the decision-making process, and I was not while it was the responsibility of the business secretary.”

He cast doubt on that today by confirming he sent a memo to David Cameron on November 19 warning that James Murdoch was “pretty furious” at Vince Cable’s decision to refer the BSkyB takeover to OfCom.

Mr Hunt suggests in the memo that he, Mr Cable, Mr Cameron and Nick Clegg have a meeting about the issue.

He told the inquiry today: “I now realise it would not have been possible for Vince Cable to attend such a meeting”, suggesting that he wasn’t allowed to intervene, even though he clearly wanted to, despite legal advice that it would be “unwise”.

More damning, perhaps, are the text messages Mr Hunt sent to Andy Coulson and George Osborne hours before the Business Secretary was stripped of his BSkyB responsibilities.

Mr Hunt was directly relaying James Murdoch’s thoughts to the Chancellor and telling Mr Coulson, then Mr Cameron’s director of communications: “I am seriously worried we are going to screw this up.”

That suggests that the culture secretary was trying to position himself at the heart of the BSky bid process while Mr Cable was just about still in charge of it.

On 25 April Mr Hunt also told MPs: “The contact that I had with Fred Michel was only at official meetings that were minuted with other people present.”

While there’s little dispute that Mr Michel did exaggerate the contact he had with the culture secretary, that phrase doesn’t square with what we heard today.

Mr Hunt confirmed a string of text messages had passed between the two men. That contradicts the letter of what he told parliament, but it has to be said that the texts were of a chirpy social nature and didn’t touch on the BSkyB bid.

At one stage Mr Hunt replied to a text by saying: “Hope U understand why we have to have the long process. Let’s meet up when things are resolved.”

So Mr Hunt appears to have been wrong in what he told MPs, but that may be something of a technicality rather than a resigning matter.

Was he biased in favour of the Murdochs?

Mr Hunt admitted today that he was “sympathetic” to the News Corp bid if not “supportive”. Indeed, he could hardly have said otherwise given the tone of some of the emails he sent to James Murdoch.

Just hours before taking over responsibility for BSky bid he texted Mr Murdoch to say: “Great news on Brussels. Just Ofcom to go!” – a reference to the European Commission clearing the takeover bid.

But Mr Hunt’s case is that he was able to put his sympathy to one side and make an unbiased decision about whether to allow the BSkyB deal to go ahead.

And there was no smoking gun in today’s evidence that proved otherwise.

Mr Hunt repeated the fact that he had sought independent advice from OfCom and the Office of Fair Trading and followed their advice on how to handle the bid,  and took decsions that angered the Murdochs.

By Patrick Worrall