LONDON — Few seem to be enjoying the management meltdown at the venerable BBC more than Rupert Murdoch, the News Corp. chief whose rival British newspapers have been caught up in their own lengthy, embarrassing and expensive phone-hacking scandal.

But the troubles for both media organizations highlight that the news industry in Britain is at rock-bottom in public esteem, and could face increased restrictions from the government of Prime Minister David Cameron, which appears convinced it has been unable to police itself.

The British Broadcasting Corp. has moved into full-bore damage control since it retracted mistaken allegations by its marquee news program that a politician sexually abused children. That serious mistake followed the BBC’s earlier failure to report on widespread child sex abuse allegations against one of its biggest stars, the late Jimmy Savile.

The scandal follows several years of turmoil over the phone-hacking scandal, which exploded with the discovery that employees of Murdoch’s News of the World tabloid hacked into a kidnapped girl’s mobile phone. The scandal widened when scores of celebrities, sports stars and politicians said they, too, had been hacked. The tabloid folded, Murdoch’s media paid out millions in compensation and still faces scores of lawsuits. Several news executives have been arrested.

A report due this month from Lord Justice Brian Leveson, based on months of jarring testimony about wrongdoing by Murdoch’s reporters and others, may prompt the government to impose statutory regulation on the British print press, which is overseen by an industry watchdog.

Many say the reputation of the British media is at an all-time low.

BBC chief George Entwistle resigned this weekend, and on Monday the head of news, Helen Boaden, and deputy Stephen Mitchell were temporarily removed from their positions, though the broadcaster said neither were implicated in the errors involving its child sex abuse reports.

Iain Overton, who was involved in preparing the “Newsnight” story about the politician, resigned Monday as editor of the Bureau of Investigative Journalism, a nonprofit muckraking group that works with several news organizations.

Further resignations or suspensions at the BBC are likely as the investigation develops.