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Story highlights

NEW: Murdoch should reconsider his bid to take over BSkyB given "revulsion" over hacking, Deputy PM Clegg says

The woman who edited the News of the World should resign, a lawyer for Milly Dowler's family says

Police may question Rebekah Brooks, the paper's former editor, in the coming weeks, a source says

Sunday saw the final edition of the 168-year-old News of the World, which folded over phone hacking

London (CNN) – Media baron Rupert Murdoch has not apologized to the family of a murdered British teenage girl whose phone messages were illegally intercepted by people working for his News of the World newspaper, a lawyer for the girl’s family said Monday.

The scandal over the hacking of Milly Dowler’s phone and allegations that terror victims and fallen troops may also have been targeted forced the best-selling 168-year-old newspaper to close up shop this weekend.

Rebekah Brooks, who was editor of the newspaper at the time of the Dowler hacking, should resign, Dowler family lawyer Mark Lewis said Monday.

“She should do the honorable thing,” Lewis said. “She was editor at the time Milly was taken. She should take editorial responsibility” for the actions of her journalists, Lewis said.

Brooks has since been promoted to chief executive of News International, the company that publishes Murdoch’s British newspapers. Murdoch has stood by her so far.

She may be questioned by police about the scandal in the coming weeks, a News International source told CNN Monday.

The source emphasized that Brooks would be interviewed as a witness, not a suspect, if police do question her, and rejected British press reports that the questioning would take place Monday.

The source asked not to be named discussing internal company business.

Dowler’s mother and sister met Britain’s deputy prime minister Nick Clegg Monday, keeping the scandal in the public eye despite the abrupt closure of the best-selling tabloid on Sunday.

They are due to sit down with Labour leader Ed Miliband on Tuesday and Prime Minister David Cameron, a Conservative, on Wednesday, lawyer Lewis said.

Rupert Murdoch flew into London Sunday, hours after the final edition of the News of the World hit the stands.

The scandal could affect his attempt to take full control of British satellite broadcaster BSkyB, with Clegg Monday urging him to “reconsider” the bid in light of public “revulsion” at the phone-hacking.

Clegg also said: “We owe it to the Dowlers” to get the bottom of what happened.

Murdoch was seen reading the last issue of the best-selling newspaper that launched his career as an international press baron as he arrived at the headquarters of News International, the British newspaper-publishing subsidiary of his News Corporation.

The accusation last week that people working for News of the World illegally listened to phone messages left for Milly Dowler, 13, between her disappearance and the discovery of her body in 2002, proved a tipping point in the scandal.

The Dowlers were deeply upset by the “self-congratulatory” final issue of the 168-year-old newspaper, Lewis said.

“The front cover would have been so much better if it said ‘sorry.’” he said. “There is nothing in that newspaper that has the good grace to say, ‘We really got it wrong and want to say sorry to these people.’”

Murdoch’s son James, the chief executive of News International, announced Thursday that the paper would close.

The News of the World struck a wistful yet proud tone in its final editorial Sunday, and repeated its owner’s apology for the criminal activities that brought the paper down.

“Phones were hacked, and for that this newspaper is truly sorry,” it said in an unsigned piece. “There is no justification for this appalling wrongdoing.”

The paper welcomed Cameron’s call for two different inquiries, one into how police investigated the allegations of phone hacking, and a separate one into the ethics and standards of British journalists.

Separately, police are already conducting their second investigation into the hacking itself.

Those ensnared in the police investigation include Andy Coulson, a former editor of the paper and an ex-communications director for Cameron. He and the paper’s former royal correspondent, Clive Goodman, as well as a 63-year-old man were all arrested Friday in connection with allegations of corruption.

Both Coulson and Goodman were released on bail late Friday. The third man, who was not named, was freed on bail Saturday morning. All three were ordered to report to police in October.

The scandal has prompted questions over the British prime minister’s judgment.

Cameron hired Coulson following the journalist’s resignation as editor of News of the World after Goodman and a private investigator, Glenn Mulcaire, were jailed in 2007 over hacking.

Coulson has always maintained he did not know about Goodman and Mulcaire’s use of illegal methods to get information about Prince William and other high-profile figures, but quit because the crime happened when he ran the paper.

British Culture Secretary Jeremy Hunt will consider the impact of the News of the World’s closure as he reviews its bid for BSkyB, his office said Friday.

Police are also investigating evidence that a senior News International executive may have deleted millions of e-mails from an internal archive, according to legal sources cited by the Guardian newspaper.

The decision to close the News of the World followed accusations that it illegally eavesdropped on the phone messages of murder and terrorist victims, politicians and celebrities, and claims it may have bribed police officers. Police said Thursday they had identified almost 4,000 potential targets of hacking.

Downing Street on Saturday confirmed that Cameron has approached the United Kingdom’s judiciary to suggest names for the judge to lead the inquiry into the News of the World hacking claims.

News of the World was the first British national newspaper Rupert Murdoch bought, in 1969, as he began to propel himself from Australian newspaper proprietor to international media magnate.

In addition to owning News of the World, News International owns the Sun, the Times and the Sunday Times in Britain.

Murdoch’s News Corporation also encompasses Fox News, the Wall Street Journal, the New York Post and Harper Collins publishers.