Alongside photographs of her husband and his horses in Rebekah Brooks's grand News International office is a pen and ink sketch of an old man with a twinkle in his eye. The A5-sized picture could have been a portrait of her father but it is actually of her boss, Rupert Murdoch.

Few executives at News Corporation enjoyed the closeness that Brooks did to the Murdoch family – as well as her relationship with Rupert after 22 years with the company, she spent holidays and festive dinners with his two UK-based children, James and Elisabeth. But what the departure of Brooks shows is that when it comes to business and the Murdochs, blood is still thicker than water. Her surname meant she was always dispensable, in the end.

But her belated resignation has only intensified the spotlight on James Murdoch, her direct boss as head of News Corp outside the US. This is nothing less than a fight for the survival of News Corp's heir apparent, and the notion that one of the largest media companies in the world can still be run like a dynasty.

"This is the beginning of the end for the whole dynastic thing," said someone who has worked closely with the Murdochs, but who did not wish to be named. "A head of steam is growing now that if News Corporation is to have a future, the Murdochs must be remote and reduced in number."

So grave is the current crisis that Rupert's four oldest children – James, Lachlan, still a board member despite quitting to run his own business in Australia, Elisabeth, whose independent production company was bought by News Corp this year, and Prudence, the only one without a senior position in the business – converged on London for a crisis meeting this week.

"Of course there's tension in the family," said another close source. "The business is facing major reputational issues."

Under a trust arrangement negotiated by their mother, Rupert's second wife, Anna, the four children will take the lion's share of their father's stake in News Corp. And in March, when Rupert turned 80, the regular quarterly meetings of what is essentially a minority shareholder group started to discuss the patriarchal legacy.

Murdoch Sr had just anointed James, at 38 his youngest son, as his successor by making him deputy chief operating officer of the whole company, learning at the foot of Chase Carey, a News Corp veteran. "It's part of the overall family plan to have James mostly in charge," said David Joyce, an analyst at Miller Tabak in New York at the time.

James's admission last week that he approved the £700,000 payment to Gordon Taylor without having "the full picture" has damaged this reputation for being in charge. "There were three people in that room when the payment [to Gordon Taylor] was signed off: James Murdoch, Colin Myler and Tom Crone," said Professor Brian Cathcart, professor of journalism at Kingston University and a member of the Hacked Off campaign group. "Now two of them are no longer employed by the company."

This week's meeting with his three siblings and father focused on the phone-hacking scandal. James was to move to New York this summer, while keeping a home in the UK as well as responsibility for the UK business.

"The succession has to be in doubt," said Cathcart. "If you were a News Corporation shareholder, you must question whether this company is safe in the hands of someone who has so mishandled the UK operation."

Astonishingly, Rupert Murdoch used an interview in the Wall Street Journal, his first since events began, to praise his son's management of a crisis that has so far led to the collapse of a long-cherished takeover, the closure of a 168-year-old newspaper and the departure of Brooks.

Events had, he claimed, been managed "extremely well in every way possible", with the company making just "minor mistakes". Such remarks have not helped instil confidence that Rupert Murdoch is coping with the crisis now so close to his progeny. "The fact that he is running around London in a Jimmy Savile outfit shows that he's lost the plot," said one former executive who refused to be named.

It is James who is most vulnerable. As well as his involvement in the phone-hacking scandal, institutional investors have started to flex their muscles in Sky, a publicly listed company in which the Murdochs have a majority vote of 39%. Some are already understood to have voiced their concerns to independent directors, including Nicholas Ferguson, about Murdoch's role as chairman of a £12bn satellite business, given the continuing investigations.

Sky insiders also pointed out that the arrival of Tom Mockridge to replace Brooks introduces someone who could take the reins as BSkyB chairman almost immediately, given his experience at Sky Italia. Mockridge was in line to succeed Tony Ball when James was controversially given the job of chief executive in 2003.

Where the real pressure comes, however, is in News Corp's US business.

The ongoing scandal has led a group of dissident shareholders in News Corp to renew their complaints against the company. In March, Amalgamated Bank, a trustee for several investment funds, filed a lawsuit that accused Rupert Murdoch of treating News Corp "like a wholly owned family candy store" after paying $675m for Elisabeth Murdoch's production business, Shine. Independent shareholders, who own 61% of the business, were "paying for nepotism" given the unusually high multiple paid for a business with revenues of £258m in 2009.

Last week, as details of the Milly Dowler phone hacking emerged, Jay Eisenhofer, counsel to the group, renewed its complaint about corporate governance. "News Corp's behaviour has become an egregious collection of nepotism and corporate governance failures, with a board completely unwilling to provide even the slightest level of adult supervision."

The lawsuit, by a relatively minor shareholder, has been dismissed by the company as without merit. During previous complaints about corporate governance, shareholders typically showed themselves willing to countenance senior involvement of the boss's children because of his success in creating a $50bn multinational. Yet an FBI investigation into allegations that phones belonging to victims of 9/11 were hacked into, calls by politicians for bribery investigations, and possible fines under the US Foreign Corrupt Practices Act for illegal payments to sources are all combining to make such shareholders jittery.

"Politicians are not really interested in crossing Rupert Murdoch and being targeted by Fox News," said Melanie Sloan, executive director of Citizens for Responsibility and Ethics in Washington, which is calling for a congressional investigation into News Corp. "However, 9/11 is part of the US consciousness in a way that cannot be underplayed. If it came to a choice between taking sides with Murdoch or with the victims of 9/11, there'd be no choice."

Given this uncertainty, Elisabeth Murdoch faces an uphill struggle when her attempt to finally join the News Corp board comes before shareholders later this year. "She can kiss that goodbye," said one small shareholder, who refused to be named.

The owner of Shine flew off for a summer holiday with husband, PR boss Matthew Freud, on Friday, but not before denying a story that she had criticised Brooks, a close friend, for "fucking the company". The failure to gain a seat on the board is hardly likely to stop any Murdoch family member having their say, of course. She has been an observer for several years anyway.

The family's involvement in the business, natural given their huge financial stake, has prompted many to question the future of the declining and now tainted newspaper business. James, a sometimes awkward technocrat, is more at home with the technology of a satellite platform business than with the declining print business, while Elisabeth has rarely worked outside television. Lachlan quit as an executive in 2005 and has failed to win significant plaudits with his Australian ventures.

Few family members have talked disrespectfully of the print business so beloved of their father; James tends to refer to newspapers as "products".

They could, of course, be simply listening to the views of other shareholders. One shareholder has suggested that the group's newspaper assets be hived off into a "Murdoch publications" trust, leaving the more profitable bits of the empire to the market. Whether such a future would live up to Rupert's idea of leaving his children a proper legacy, of course, remains to be seen.