Alex Salmond has always claimed that his dealings with News International were all about jobs and inward investment for Scotland.

The emails that came to light at the Leveson inquiry yesterday paint that relationship in an entirely different light and leave the First Minister and his team with questions to answer.

The emails come from the computer of Frederic Michel, News Corporation's head of public affairs, and suggest that the First Minister had offered to lobby the UK Government in favour of News Corp's controversial bid to take control of satellite broadcaster BSkyB. One claims that Mr Salmond would call Culture Secretary Jeremy Hunt about the matter "whenever we need him to". The communications also make clear the SNP leader's delight at the decision by the Scottish Sun to back the Nationalists in the Scottish Parliamentary elections of 2011.

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In evidence yesterday James Murdoch denied Mr Salmond's support for the bid was a quid pro quo for favourable coverage. However, given the tone of the emails, the First Minister has much explaining to do. He should publish any written and email correspondence with News Corp executives concerning this matter. At the very least, there appears to have been an unhealthily cosy relationship between the Scottish Government and a company mired in the phone-hacking scandal.

In the event, the bid for BSkyB was withdrawn after that scandal forced the closure of the News of the World. Nevertheless, Mr Salmond had clearly been keen to help that bid succeed. Why? Because it was in the interests of Scottish television viewers and future investment or as a thank-you for the Murdochs' political support? It is precisely issues like these that the Leveson inquiry was set up to probe and the First Minister's appearance will be keenly anticipated.

He is a skilful and sure-footed politician. If he has a potential weakness, it is his hubris and a tendency to be dazzled by the rich and powerful. His admiration for Fred Goodwin rebounded on him badly, as did his dalliance with Donald Trump. Mr Salmond's relationship with Rupert Murdoch has the appearance of a Faustian bargain in which the Murdochs took revenge on the Conservatives' for abandoning them by supporting the SNP and the SNP took a pot short at the BBC, which it accuses of being pro-Unionist, by backing Sky. Yet one lesson of Leveson should be the desirability in a parliamentary democracy of a distance between politicians and media moguls.

The Culture Secretary is in far deeper trouble. After assuming oversight of the bid from Vince Cable, Mr Hunt rightly stated that his was a quasi-judicial role, requiring complete impartiality. However, yesterday's evidence appeared to show that he was as biased in favour of News Corp as Dr Cable had been against it. He should consider his position.

As for the Prime Minister, his "omnishambles" expanded yet further yesterday with the admission from James Murdoch that the two men discussed New Corp's bid at a jolly Christmas dinner at the home of News International chief executive Rebekah Brooks in December 2010 at the height of the controversy surrounding it. This is serious. The Prime Minister has always denied that there was an "inappropriate conversation" that night. Recent events call into question his competence. Yesterday's evidence raises a question about his integrity.