Rupert Murdoch has long sought to add Sky, the British satellite and news giant, to his stable of global media outlets that includes movie studios, newspapers and cable networks like Fox News.

Yet after the sexual harassment scandal at Fox News that led to the ouster of Roger Ailes, its chairman, and the revelation of several settlements involving Bill O’Reilly and allegations of inappropriate behavior, Mr. Murdoch and 21st Century Fox now face renewed scrutiny over their plans to buy the 61 percent stake in Sky that they do not own.

On Friday, European officials gave their blessing to the deal, which is worth 11.2 billion pounds, or $13.9 billion. But the battle will come to a head when a British regulator rules next month on whether the proposed deal gives Mr. Murdoch, who already controls several national newspapers, too much clout over the British media landscape.

British officials also must decide if 21st Century Fox and its executives pass a “fit and proper test,” or judgment on whether the people who will run the merged company are fit to do so. That includes particular attention to James Murdoch, one of Mr. Murdoch’s sons, who is the chief executive of 21st Century Fox.

It remains unclear whether British regulators will be influenced by the recent scandals at Fox News, including the accusations that Mr. O’Reilly sexually harassed several women. Mr. O’Reilly denies the claims.

But the increased focus by British regulators on the actions of 21st Century Fox officials comes at a difficult time for the company. It also is likely to rekindle memories of the phone hacking scandal in Britain and criticism by some of the country’s officials of how James Murdoch handled it.

“It’s hard to predict what’s going to happen because we don’t have a great track record in cases like this,” said Lorna Woods, a media law professor at the University of Essex. The “fit and proper test isn’t limited to Britain,” she said. Regulators “have the potential to look at a person’s actions wherever they take place.”

Ofcom, the British regulator that must rule by May 16, declined to comment on the specifics of the case, saying it would take into account any relevant misconduct.

21st Century Fox denied that its proposed takeover would fail the fit and proper standards. It said James Murdoch had been the chairman of Sky since early 2016, and if British officials were concerned, they would have investigated the issue by now.

“I’d be surprised if it materially affected the regulators’ view,” Martin Gilbert, Sky’s deputy chairman, said in an interview, in reference to the potential impact of troubles at Fox News on the proposed takeover.

Legal experts note that the fit and proper standards are ill-defined and that it is hard to establish a precedent from the few previous cases that are in any way similar to the proposed takeover of Sky.

In fact, the most similar regulatory ruling also centered on the efforts by News Corporation, 21st Century Fox’s predecessor, to buy Sky in 2010. The company was eventually forced to abandon its bid in the wake of the phone hacking scandal.

In that decision, the British regulator ruled that Sky remained a fit and proper holder of the country’s broadcast licenses. It also criticized the conduct of James Murdoch in the phone hacking controversy, but it said there was no evidence of his involvement in any illegal activity. He was then chairman of the company’s British newspaper group.

“We consider James Murdoch’s conduct to be both difficult to comprehend and ill-judged,” the regulator wrote in 2012. His conduct “fell short of the exercise of responsibility to be expected of him as C.E.O. and chairman.”

In response, 21st Century Fox says that the company has significantly improved its corporate governance since its previous bid for Sky, and that the spinoff of the newspaper operations controlled by Rupert Murdoch in 2013 had cemented these changes.

While 21st Century Fox remains confident that it will finally take control of Sky, its critics are also calling on the British regulator to think hard about the potential dominance that the Murdochs may exert over the country’s media if the deal is approved.

The proposed takeover would also be subject to the approval of the British government after the regulator completes its review next month.

The Murdoch family owns 39 percent stakes in both 21st Century Fox and News Corporation, the group that owns The Wall Street Journal, The Times of London and several other publications.

Martin Moore, director of the Center for the Study of Media, Communication and Power at King’s College London, said 21st Century Fox’s proposed acquisition of Sky and its large British news operations could further expand Rupert Murdoch’s control of the British media industry.

The company disputes this, saying digital platforms like of Google and Facebook offer new media competition that did not exist when it last tried to buy Sky in 2010.

“Of course we’ve seen an expansion in how news can be distributed on these digital platforms,” Mr. Moore said. “But if Sky and News Corp are effectively merged under the Murdoch umbrella, we can expect them to follow a similar editorial stance. How does that help media plurality in Britain?”