Preview: What to expect from Leveson’s biggest week

Some of Britain's biggest political names are giving evidence at the Leveson inquiry this week. Here's a summary of the areas where they're likely to face the toughest questions.

Monday: Gordon Brown

Central to Gordon Brown's evidence will be questions about whether New Labour had excessive contact with the media – especially Rupert Murdoch and his colleagues.

Inquiry counsel Robert Jay will probably adopt a chronological approach to questioning which will see his part in the construction of Labour's heavy media-focus analysed in detail, initially. This line of questioning could culminate in a look at whether Brown was obsessed with the media and responding to the 24-hour news agenda, as many have claimed.

It is the bitter breakdown of relations between News International and Brown's struggling government which could generate the most controversy, however.

Rebekah Brooks claims Brown was "incredibly aggressive" after the Sun switched its allegiance to the Tories in late September 2009. He will be asked questions about his attitude to the war in Afghanistan, as this was a major part of the Sun's decision to break with him.

Brown was described as "unbalanced" in a conversation Murdoch claims took place as it emerged the Sun was switching sides. Brown denies any such conversation ever happened, thus rebutting Murdoch's claim that Brown promised to "declare war" on News International. Brown says he only ever spoke to the paper once in his final year.

The row over the 2006 story which broke the news that Brown's son had cystic fibrosis will also be addressed again. Brown had claimed the information could only have been obtained via some form of hacking. Murdoch and Brooks admitted under questioning that a father from the same hospital had given the newspaper the information – and that he was linked with a prominent cystic fibrosis charity.

The slumber party hosted by Sarah Brown for Brooks, Murdoch's wife Wendi Deng and daughter Elisabeth could also be raised.

Brown could also be asked about the interview with Andrew Marr in which the BBC journalist questioned him about whether he used prescription painkillers to "get through" the day.

Monday: George Osborne

The chancellor was originally only supposed to give written evidence to the inquiry, but his influence in a number of key issues has become increasingly clear.

First and foremost is his role in the handling of News Corp's takeover bid for BSkyB, after a Telegraph sting led to Vince Cable being stripped of responsibility. Last week it emerged he played a significant role in the decision to hand culture secretary Jeremy Hunt responsibility for the bid. He texted Hunt: "I hope you like our solution." This raises questions about whether Hunt, who was known to broadly favour the takeover, was appointed to please News Corp.

Then there are questions to be asked about the recruitment process in which former News of the World editor Andy Coulson became David Cameron's head of communications. Osborne had a key part in this, approaching Coulson for the job.

Mark Lewis, a solicitor representing victims of phone-hacking, has told the Leveson inquiry it may be that Osborne felt obliged to help Coulson after Coulson had done him a favour: specifically, putting a "gloss" on stories about former dominatrix Natalie Rowe claiming Osborne took cocaine in the 1990s.

Tuesday: Sir John Major

The former Conservative prime minister will face questions about his government's failure to reform regulation of the press. Former Cabinet minister Lord Brooke has already told Leveson that the government was "extremely reluctant" to back the findings of a 1993 report on media intrusion, the Calcutt report, which called for statutory regulation.

Lord Brooke's successor, Stephen Dorrell, has told Leveson he had been instructed to limit the damage of the government deciding not taking any steps to introduce real reform. His orders were to "do nothing" and go about doing it "in the least bad way".

Why did Sir John shy away from taking on the issue? How frank will he be in explaining the dilemmas that Britain's weakest prime minister in recent times faced?

Tuesday: Ed Miliband

The leader of the opposition has made much political hay at the revelations of the Leveson inquiry so far. Now Ed Miliband is giving evidence himself. His spin doctors will tell him this is an opportunity. He will do all he can to use this platform to consolidate his attacks on Cameron's government. But this evidence session could also pose a threat.

It is Miliband's involvement in the New Labour he has worked so hard to distance himself from which will be awkward for the Labour leader. Miliband was a close ally of Gordon Brown, whose government did more than of its predecessors to court the press. The opposition party has worked hard to present itself as being above the kind of inappropriately close relationships which the Tories have with Murdoch. Reminders about Miliband's New Labour past could prove very politically damaging.

Jay has a number of avenues to explore here. He could explore the sudden, dramatic change in Miliband's behaviour before and after the phone-hacking scandal broke. He might point out that Miliband met News International executives 15 times since the last general election. A 2011 summer party in Holland Park hosted by Rupert Murdoch could be raised: Miliband was reportedly almost the last guest to leave.

Tuesday: Harriet Harman

"Liverpool's already kicked out The Sun," Harriet Harman said in Liverpool last year. "It is time for all the Murdoch papers to be kicked out of Britain." Her language since the phone-hacking scandal broke has been uncompromising, that's for sure. But she was more balanced while in government. As a senior figure in the New Labour government her insight into its attitude towards the Murdoch empire will be fascinating.

Harman's priority will be keeping the focus on the current situation as much as possible. Her party leader will be stealing the headlines, but she too has an opportunity to once again stick the knife in against culture secretary Jeremy Hunt, her opposite number in the Commons.

Wednesday: Nick Clegg

The coalition's deputy prime minister will be walking a tricky tightrope at Leveson. As leader of the Liberal Democrats his party has been the least embroiled with the Murdochs in recent decades, because of its relative political irrelevance. Clegg's speeches as leader in opposition placed Labour and the Tories as defenders of an Establishment two-party system. He will be looking to continue those attacks, raising coalition tensions further in the process.

"My view, hardened by two years on the inside, is that Britain is not broken at all," he said two weeks ago.

"It is the British establishment that is broken. It is the institutions at the top that have let down the people."

This is a risky approach, for – having arrived in government – he could be attacked for having instantly converted to Establishment behaviour. He has played tennis with Murdoch's chief lobbyist Fred Michel. His special adviser has exchanged texts with Mr Michel.

Clegg might be able to get away with broad-brush attacks on the two main parties, but he will have to be more careful when it comes to specific members of his government who are under fire. Like Jeremy Hunt. Clegg, who has been evasive on whether Hunt has his support, will be forced to give a clearer view of Hunt's performance at Leveson two weeks ago. Does he think the culture secretary acted inappropriately?

Wednesday: Alex Salmond

The Scottish first minister faces a challenging session at Leveson after a particularly damaging text emerged in April, suggesting a quid pro quo had been agreed between the SNP and the Scottish Sun, a News Corp title.

Fred Michel had texted News Corp chief James Murdoch telling him Salmond's special adviser would "call Hunt whenever we need him to". Was this a case of Salmond offering to lobby the UK government in favour of the BSkyB takeover bid, in return for support from the newspaper? Salmond has already issued vigorous denials that this is the case – and so did Murdoch when giving evidence. But the question will doubtless be asked once again.

Even if that denial works, Salmond will have to play down his very earnest courting of the Murdochs, which has actually continued even after the phone-hacking scandal broke.

Thursday: David Cameron

For the prime minister, the inquiry he set up at the height of the phone-hacking scandal last year is nothing less than a trial of his conduct. Put simply, no one has more to lose than the leader of the Conservative party.

Cameron is vulnerable on three fronts. Firstly comes the phone-hacking scandal, linked to the prime minister by his decision to hire News of the World's former editor Andy Coulson as his director of communications. This is partly a question of judgement. In the light of what we know now, was this the Tory leader's worst decision? Cameron can expect detailed questions about the vetting process used on Coulson. Even at its most rudimentary, how much did Cameron probe Coulson's knowledge of phone-hacking at the News of the World?

Then comes their discussion of the issue while Cameron was in No 10. Coulson told Leveson that he had only discussed phone-hacking with Cameron briefly while in office. How much did he know about what had really gone on at the tabloid?

Cameron's second vulnerability is over the cosiness of his relationship with the Murdochs and their cronies. That seems to be summed up in the texts which Cameron sent to Rebekah Brooks, signing them 'lol' (he meant lots of love). The prime minister acted just the same as his many predecessors in dealing with the Murdochs. Unlike Miliband, who was not in a senior enough position, or Clegg, who was out of power and therefore relevance, Cameron spent many years becoming friendly with the media mogul, his family and close allies. The prime minister should expect a series of questions examining his actions and motivations during the period before the summer of 2011, when amid the heat of the phone-hacking scandal politicians were finally able to make a break with the past for good.

The final vulnerability comes over the government's handling of News Corp's BSkyB takeover bid. This is not just about the conduct of Jeremy Hunt, who Cameron has resolutely defended. It is about Cameron's decision to hand the obviously pro-takeover Hunt responsibility for the decision in the first place, and his reluctance to refer Hunt to the independent adviser on ministerial behaviour. His protection of Hunt is widely viewed as being a reflection of the weakness of his own position. So there's a strong sense Thursday is going to be about damage limitation.

The temptation to steal the headlines by hinting at his own attitudes to the future of press regulation – without attempting to prejudge Lord Justice Leveson's findings, of course – will be very strong.