Britain's long-running phone hacking scandal has taken a sickening twist, with claims that a tabloid newspaper hacked into the phone mail of an abducted teenage girl and may have hampered the police investigation into her disappearance.

The News of the World newspaper in London is again the target of allegations that it was involved in hacking into cellphone voicemail, this time in the case of a schoolgirl who was later found murdered. (Matt Dunham/Associated Press) Prime Minister David Cameron said Tuesday he was deeply shocked by the new charges and called for a thorough police inquiry.

"If they are true, this is a truly dreadful act and a truly dreadful situation," Cameron said of the allegations.

The case involves 13-year-old Milly Dowler, who went missing in 2002 and was murdered by a nightclub doorman who has been convicted of the crime.

The new allegations centre on the controversial News of the World tabloid, which has already seen a number of its journalists arrested for breaking into the cellphone voicemail systems of celebrities, sports figures and royal aides. The newspaper has admitted wrongdoing in those cases and made financial settlements with some of its victims, including actress Sienna Miller.

The newspaper is now accused of hacking into Dowler's voicemail and deleting several messages on her cellphone, giving her parents false hope that she was alive as well as potentially damaging the police effort to find her.

Lawyer Mark Lewis, representing the family, said he plans to sue the tabloid for its interference in the days after the girl went missing while heading home from school in Walton-on-Thames in Surrey, south of London. Her remains were found in woodlands six months later by mushroom pickers. It was not clear how long she was alive after being abducted.

Milly Dowler, 13, was first reported missing in 2002. She was later murdered by a nightclub doorman. (Surrey Police/Associated Press) "It is distress heaped upon tragedy to learn that the News of the World had no humanity at such a terrible time," Lewis said. "The fact that they were prepared to act in such a heinous way that could have jeopardized the police investigation and give them false hope is despicable."

He said someone at the newspaper should take responsibility.

The Dowler family claims a private investigator working for the paper deleted some of Milly's messages to make room for new messages. The family was told of the intrusion into her cellphone in April, but the accusations were only made public Monday.

Rebekah Brooks, chief executive of News International, which publishes the tabloid, said in an email to her staff Tuesday that the "strongest possible" actions would be taken if the charges were found to be true.

"We were all appalled and shocked when we heard about these allegations yesterday," she said. "I am sickened that these events are alleged to have happened. Not just because I was editor of the News of the World at the time, but if the accusations are true, the devastating effect on Milly Dowler's family is unforgivable."

Brooks said in the email that she had no knowledge of the alleged hacking and said she would not resign.

News International said it would be conducting its own inquiry into the allegations.

"This particular case is clearly a development of great concern and we will be conducting our own inquiries as a result. We will obviously co-operate fully with any police request on this," the company said in a statement.

News International is the main U.K. subsidiary of News Corp., where media mogul Rupert Murdoch is chief executive.

A private investigator and a royals editor who worked for News of the World were jailed in 2007 for tapping the phones of royal household staff. Five more people have been arrested since a fresh police investigation began in January.

Opposition Leader Ed Miliband of the Labour Party said Tuesday that Brooks should "consider her position" in light of the new accusations, which he said threaten to put a stain on British journalism.