For the first time we have evidence of the Murdochs exploiting their position to apparently win favours from governments

Now we come to the dark heart of this strange affair.

Critics of the Murdochs have often suspected that they have exploited their position as newspaper owners to win secret favours from governments – and the Murdochs and the politicians alike have denied it. Now, for the first time, courtesy of the volatile chain-reaction of the phone-hacking scandal, we have compelling evidence.

In 163 pages of paperwork published by the Leveson inquiry, we can see the dialogue between James Murdoch's camp and the office of Jeremy Hunt, the secretary of state for media, who held in his hands the outcome of the biggest deal in the history of the Murdochs' News Corporation, the £8bn takeover of BSkyB.

According to Tuesday's evidence, Murdoch and his lobbyist, Fred Michel, worked their way through every crack in the walls of Whitehall in search of influence and, in Hunt's office, they found friends who would supply them with information, advice and support, even as Hunt claimed to the outside world that he was being impartial and even-handed.

The evidence is likely to be disputed. These are merely Michel's versions of what was said, so they are hearsay. Furthermore, Michel has told the inquiry that his messages that claimed to report conversations with Hunt were in fact based on talking to Hunt's officials, which would mean that they are also secondhand. But, if the evidence stands up, we are looking at a story of secret and improper collusion of precisely the kind that Murdoch's critics suspected.

At a time when Hunt was required to act in the legal role of a judge overseeing Ofcom's inquiry into the bid, this evidence suggests he was secretly supplying News Corp with information about his confidential dealings with Ofcom, advising them on how to pick holes in Ofcom's arguments, allowing their adviser to help him prepare a public statement, offering to "share the political heat" with them, and repeatedly pledging his support for their position.

If proved, this pushes Hunt's political career to the edge of destruction. It cannot help him that his website currently displays an interview describing him as a cheerleader for Rupert Murdoch. But the pressure may not stop there. The question now is whether Lord Justice Leveson will order the disclosure of more emails or other evidence that could conceivably see the prime minister and his government pushed out to the edge as well.

Cameron can become embroiled in two ways. First, he faces questions about whether he had any kind of involvement in handling the bid for BSkyB, particularly during the quasi-judicial process from June 2010 to July 2011. For the first time on Tuesday, it was disclosed that Murdoch had raised the bid with him when they met at Rebekah Brooks's house two days before Christmas 2010. Previously, Cameron had refused to answer direct questions about what was discussed on this occasion. His opponents will be interested to know whether he really did keep his distance even as last year the bid was swept up in the political tornado around the phone-hacking scandal.

Second, and potentially even more serious, the prime minister would be in jeopardy if the alleged support for the BSkyB bid proved to be part of a bigger deal between the Conservative leadership and News Corp. In its crudest form, the suggestion is that the Murdochs used the Sun to make sure that Gordon Brown was driven out of Downing Street so that the incoming Conservative government could deliver them a sequence of favours – a fair wind for them to take over BSkyB; the emasculation of the much resented Ofcom; and a severe funding cut to their primary broadcasting rival, the BBC.

This was the core of the toughest exchanges on Tuesday, as Robert Jay QC, for the inquiry, laid out fragments of evidence that suggest this big deal was made, and concluded: "It all falls together, doesn't it?" In reply, James Murdoch passionately denied that he would ever link his newspaper's endorsement of a political party to the commercial interests of his company. "I simply wouldn't do business that way."

Until Tuesday, all of the evidence for the big deal was circumstantial.

We knew that both Rupert and James Murdoch had complained publicly and bitterly that Ofcom was interfering in their business. This came to a head on 26 June 2009, when Ofcom announced it wanted to force BSkyB to sell its channels to rivals at far lower prices. Ten days later, on 6 July, Cameron announced that, if elected, he would abolish Ofcom.

Similarly, the Murdochs have launched a series of lacerating attacks on the BBC, arguing that its income should be cut and its commercial activity restricted. In March 2009, Cameron called for the BBC licence fee to be frozen. In May 2009, Hunt did the same. Days after James Murdoch delivered his famous MacTaggart lecture in August 2009 – in which he renewed his attack on Ofcom as well as the BBC – Hunt met News Corp officials in New York. He then wrote an article for the Sun attacking the BBC for accepting a rise in its licence fee that year and calling on it to cut back its commercial activities.

It was disclosed on Tuesday that days later, on 10 September, James Murdoch went to a private drinking club in Mayfair for an evening meeting with Cameron, during which he told him that the Sun would back the Tories in the next election.

Murdoch also disclosed on Tuesday that the BSkyB bid had been discussed at a formal News Corp meeting in Los Angeles a few weeks before this meeting. There is no evidence at this stage, however, that the bid was mentioned to Cameron.

The Sun then used its news columns to launch a sustained attack on Gordon Brown. Five months after the election, Cameron's government slashed Ofcom's budget by 28% and cut back its role; and slashed the BBC's income by 16% and cut back its commercial activity.

Tuesday's cache of emails about the BSkyB bid appears to fit into that sequence with a neatness that will alarm the government.

It will alarm them, too, that in the political heat of last July, Cameron gave Leveson terms of reference for this part of his inquiry, which are very broad: "To inquire into ... the relationships between national newspapers and politicians, and the conduct of each."

Leveson may decide that he does need to order the disclosure of more evidence. Hunt may find a defence for his position. The government may emerge with no loss beyond that of Cameron's media adviser, Andy Coulson, who quit last year over decisions he made when editing the News of the World, well before he joined the government.

Yet as things stand, it is clearly possible that this strange affair, which began so quietly with the minor crimes of a single journalist and which has already brought acute pain and senior resignations to the Metropolitan police, the Press Complaints Commission and Murdoch's ranks in London and New York, may yet reach deep into the heart of government and do its damage there, too.