High on the list of those wounded by Britain's phone-hacking scandal is Prime Minister David Cameron

High on the list of those wounded by Britain's phone-hacking scandal is Prime Minister David Cameron, who took a further hit on Sunday with the arrest of Rebekah Brooks, the former News Corp. executive who is a friend of the U.K. leader.

Adding to the potential damage for Mr. Cameron, the scandal has simultaneously boosted the standing of Ed Miliband, leader of the opposition Labour Party, whose response has won him positive headlines in the same way as it has earned Mr. Cameron negative ones.

Ms. Brooks was arrested on Sunday in connection with the scandal, which centers on the alleged interception of mobile-phone voice-mail messages and bribes to police. That is a problem for Mr. Cameron because he has long been seen as close to Ms. Brooks, having attended her 2009 wedding and invited her twice to Chequers, the prime minister's weekend retreat, in the past 14 months. Among a list of meetings dating back to May 2010 released by Downing Street between the prime minister and Ms. Brooks, who have homes close to each other in the English county of Oxfordshire, two were listed as "social."

Ms. Brooks isn't the first person with close ties to Mr. Cameron to be arrested in the phone-hacking scandal. Earlier this month, the prime minister's former director of communications, Andy Coulson, was arrested for his alleged role in the phone hacking at the News of the World tabloid he once edited. Mr. Coulson was released on bail and hasn't been charged.

That has led the British public, opposition politicians and even members of his own party to question Mr. Cameron's judgement for hiring a man who—only months before Mr. Cameron hired him to advise the Conservative Party, when it was still in the opposition—had resigned from the News of the World after one of his reporters was jailed for phone hacking.

Mr. Cameron has said he sought and received assurances from Mr. Coulson that the phone hacking had been limited to one rogue reporter at News of the World. News Corp. executives have made the same statements to Parliament over the years, assertions that have come back to haunt them.

But Mr. Cameron was already seen as close to News Corp., having courted the company in an effort to win its election endorsement. The Downing Street release of meetings with the media showed that Mr. Cameron met with News Corp. Chairman Rupert Murdoch and his son James Murdoch , and met several times with the editors of News Corp. newspapers the Sun, Sunday Times, Times and News of the World.

"Undoubtedly, Cameron has suffered reputational damage and it has been good for Ed Miliband, who has appeared authoritative, something he hadn't till now," said Wyn Grant, politics professor at the University of Warwick.

Still, while Labour has gained percentage points in opinion polls, the Conservative Party's rating hasn't collapsed, losing only a few percentage points. Despite the knock, ultimately Mr. Cameron's destiny is more closely linked to recovery of the country's still-weak economy and to the ever-rising cost of living for cash-strapped Britons.

A Downing Street spokesman declined to comment on Ms. Brooks's arrest. Mr. Cameron recently said that politicians, including himself, have become too close to the media.

On Sunday, Mr. Miliband pressed his case harder, calling for the breakup of the elder Mr. Murdoch's U.K. media holdings, arguing that the chairman and chief executive officer of News Corp. has "too much power over British public life."

In an interview with the Observer newspaper, Mr. Miliband said he hoped to secure cross-party agreement on new rules governing media ownership that would reduce News Corp.'s market share.

"I think that we've got to look at the situation whereby one person can own more than 20% of the newspaper market, the Sky platform and Sky News," Mr. Miliband said. "I think it's unhealthy because that amount of power in one person's hands has clearly led to abuses of power within his organization."

News International publishes the Times, the Sunday Times and the Sun newspapers and, until last week, the News of the World tabloid that has been at the center of the phone-hacking accusations. News Corp. also owns The Wall Street Journal.

The Liberal Democrat Party declined to comment. The coalition government's junior party, though, has been putting it own pressure on News Corp. Last week, senior lawmakers wrote to Ofcom to ask the regulator and competition authority for the U.K. communications industries to look into whether News Corp. is a "fit and proper owner" of its remaining stake in satellite broadcaster British Sky Broadcasting Group PLC.

In a speech on Monday, Mr. Miliband is going to further push the issue and try to compare the hacking scandal with the credit crisis and the abuse of parliamentary expenses by British lawmakers.

"All are about the irresponsibility of the powerful, people who believed they were untouchable," he will say, according to excerpts of that speech.