Some shareholders have expressed doubts about whether James Murdoch, 38, should take over from his father.
On Monday, Standard & Poor's said it may cut News Corp's credit rating from the current BBB+. It put the group's ratings on creditwatch with negative implications given the business and reputational risks associated with widening legal probes in Britain and pressure for a FBI investigation in the United States.
The parliamentary committee has been pursuing the phone-hacking allegations for more than four years, saying in a report in 2010 that it was inconceivable that managers did not know about the practice.
"We intend to be calm and forensic. There will be no circus, no playing to the gallery because we really need to get to the bottom of everything that has gone on," said Farrelly, a former journalist who once worked for Reuters.
"We want to know who knew what, and when, and how wide the whole ambit of illegal activity, of which phone-hacking was only one part, went, and how far any cover up went."
In another development, police said a man believed to be former News of the World journalist Sean Hoare was found dead at his home near London on Monday. A post-mortem examination was to take place on Tuesday.
It was Hoare who told the New York Times that phone hacking at the tabloid was far more extensive than the paper had acknowledged at the time. The former show business reporter also told the BBC he was asked by Coulson, who went on to work for the prime minister, to tap phones.
News International chairman James Murdoch said earlier this month that the News of the World "made statements to parliament without being in full possession of the facts" and he is certain to be questioned on that statement.
The Murdochs are due to appear at 2:30 pm (1330 GMT), followed an hour later by a separate hearing for Brooks.
Brooks resigned as News International chief executive on Friday and was arrested by police on Sunday on suspicion of corruption and intercepting communications before being released on bail.
The Guardian newspaper said detectives were examining a computer, paperwork and a phone found in a bin near Brooks' riverside London home.
Brooks' spokesman dismissed the story as "rubbish" but said the personal computer of her husband Charlie had mistakenly got into the hands of the police. The couple were waiting to get it back after the police had examined it.
QUESTIONS FOR CAMERON
Prime Minister Cameron, who took office in May 2010, is facing the worst crisis of his premiership as his decision to hire former News of the World editor Coulson as his communications chief comes back to haunt him.
Coulson quit the paper in 2007 when the paper's royal reporter was jailed for phone hacking. Coulson said he knew nothing of the practice but took responsibility.
Coulson resigned as Cameron's spokesman in January when the long-running scandal came back to life. He was arrested earlier this month and is also free on bail.
Cameron's position has been made worse by a parting shot from London police chief Stephenson, brought low by the force's decision to hire a former News of the World deputy editor, now implicated in the scandal, as a media adviser.
Stephenson drew a subtle contrast between his decision to step down and Cameron's conduct. However, facing a parliamentary committee on Tuesday he had meant no criticism at all of the prime minister.
Few expect Cameron to quit but he appears weakened as head of a deficit-cutting coalition and might find his room for maneuver limited.
John Yates, the other senior officer to resign, was due to follow Stephenson in appearing before parliament's home affairs committee in what will be a prelude to the main event with the Murdochs.
Computer hackers turned the tables on the media group when some broke into the website of Rupert Murdoch's best-selling British tabloid, The Sun. They altered the front page to show a fake report about the media mogul's death.