Cameron's own image has been tarnished by his support for his ex-spokesman Andy Coulson, a former News of the World editor who was arrested earlier this month.
Judge Brian Leveson, who prosecuted serial killer Rosemary West in the 1990s, is leading the inquiry into the phone-hacking allegations, media ethics, and the relationship between media organizations, police and politicians.
On Thursday, he urged all parties to consider the public interest, not only their own. He has authority to call any party to give evidence under oath to the inquiry, which is planned to take about a year.
"It may be tempting for a number of people to close ranks and suggest that the problem is or was local to a small group of journalists then operating at the News of the World," he told a news conference in London.
"I would encourage all to take a wider picture of the public good and help me grapple with the length, width and depth of the problem."
Shareholders in News Corp have called for an overhaul of corporate governance as the crisis spreads.
A spokesman for Co-Operative Asset Management, a small investor in both News Corp and BSkyB, said on Thursday: "We believe radical reform is needed at both companies but at News Corp in particular, and indeed in the newspaper industry in the UK to stamp out the kind of illegal and grossly invasive practices that are alleged."
Thursday's BSkyB board meeting in London took place on the eve of the company's quarterly results announcement. The results are expected to continue a strong run for the company, and investors hope a special dividend will also be announced.
The board had said for the last year that it would not be appropriate to consider such a measure while it was a takeover target, and many brokers are stoking hopes of a payout now.
Analyst Ian Whittaker of Liberum Capital cautioned, however, that the moment may be too sensitive politically.
"Given the fast-moving events of the past two weeks, management may feel now is not the right time to announce a special dividend, especially given the potential complications of returning a significant level of cash back to its 39 percent shareholder News Corp," he said.
"Historically, BSkyB management have emphasized investment over a return of cash back."