Tony Blair is back at centre stage as he appears at the Leveson inquiry to be questioned about his relations with the media.

The former British prime minister is likely to be asked about the nature of his and his government's links with Rupert Murdoch's media empire during his 13 years at the helm of the Labour party, including a decade in Downing Street.

He is expected to face questions over whether he allowed his relationship with Murdoch and News International to become too close, as his former lieutenant Lord Mandelson told the inquiry last week. Lord Mandelson said it was "arguably the case ... that personal relationships between Mr Blair, [Gordon] Brown and Rupert Murdoch became closer than was wise."

Blair famously flew to Hayman Island in Australia to address News Corp executives in 1995 as part of a Labour strategy to gain a hearing with newspapers that had savaged previous leaders Michael Foot and Neil Kinnock.

It emerged in 2010 that he formed a close enough relationship with Murdoch to become the godfather to one of the media tycoon's children in 2010.

Blair's appearance comes at the start of a high-profile week for the Leveson inquiry, with the beleaguered culture secretary, Jeremy Hunt, due to give evidence on Thursday. Hunt will also face a grilling over his office's links with Murdoch's News Corp, particularly during its bid to take over the satellite broadcaster BSkyB.

He will be challenged over whether his public expressions of support for the bid were compatible with the quasi-judicial role he was given by the prime minister, David Cameron.

There was unconfirmed speculation over the weekend that Cameron is due to appear two weeks later, on Thursday 14 June, and that George Osborne, the chancellor, might also be called.

The education secretary, Michael Gove, and the home secretary, Theresa May, will appear on Tuesday and the justice secretary, Kenneth Clarke, on Wednesday.

Also due to give evidence on Wednesday is the business secretary, Vince Cable, who was stripped of the role of deciding whether the bid could proceed after he was secretly recorded saying he had "declared war" on Murdoch.

Hunt had asked for his appearance before the inquiry to be brought forward so he could give his side of the story as soon as possible, but was rebuffed by Lord Justice Leveson.

The inquiry has been presented with a cache of emails showing the News Corp lobbyist Frédéric Michel received inside information about the Department for Culture, Media and Sport's handling of the bid from Hunt's former special adviser, Adam Smith, who quit in April after admitting he went too far in acting as a point of contact with the company.

Last week, the inquiry published a memo sent by the culture secretary to Cameron in November 2010, weeks before he took on the quasi-judicial role, in which he appeared to be making the case for News Corp's bid to go ahead. Hunt insists he oversaw the process "with scrupulous fairness throughout" and has received strong backing from the prime minister.

But Cameron has also said that if anything arises from the inquiry that suggests the ministerial code might have been breached, he will call in his independent ethics adviser, Sir Alex Allan, or take immediate action himself.