The scandal over claims that British tabloid News of the World hacked the phone of murdered teenager Milly Dowler took a new turn as it emerged that families of the 7/7 London bombings may also have been targeted.

Graham Foulkes, whose 22-year-old son David was among the 52 people killed, was among those warned by detectives that they featured on a list of possible hacking victims.

Detectives also confirmed that they had contacted the parents of murdered schoolgirls Holly Wells and Jessica Chapman, as part of the investigation into phone hacking at the top-selling Sunday tabloid.

In a further twist late Tuesday Prime Minister David Cameron was dragged into the crisis when the newspaper's owners, News International, revealed that they had forwarded evidence to the police which alleged former editor Andy Coulson had authorized payments to police in return for information.

Coulson, who was editor between 2003 and 2007, also worked as Cameron's director of communications from 2007 to 2011 when he resigned as allegations emerged, although he has always denied any wrongdoing.

Cameron said on Monday police should pursue their investigation into the Dowler claims in "the most vigorous way".

He said police "should feel they should investigate this without any fear, without any favour, without any worry about where the evidence should lead them. They should pursue this in the most vigorous way that they can".

"If they are true, this is a truly dreadful act and a truly dreadful situation. What I've read in the papers is quite, quite shocking," Cameron told a press conference during a visit to Afghanistan.

News International chief Rebekah Brooks, who was editor of the News of the World at the time of Dowler's disappearance in 2002, told staff that the allegations were "sickening" and "almost too horrific to believe".

"If the allegations are proved to be true then I can promise the strongest possible action will be taken," said Brooks.

The tabloid has been dogged by claims of phone hacking ever since its royal editor and private investigator Glenn Mulcaire were jailed for the practice in 2007, and a new investigation was launched in January amid a wave of fresh allegations.

Dowler disappeared aged 13 on her way home from school near London, sparking a high-profile search. Her bones were found six months later, although it was not until last month that her killer Levi Bellfield was convicted.

According to the Guardian, private investigators and journalists listened to increasingly desperate messages on Dowler's phone left by her parents and friends as the days went by without any word from her.

When her voicemail box became full, they even deleted several messages to make room for new ones -- an action that her loved ones and police mistakenly took as proof that Dowler was still alive and using her phone, the report said.

Police refused to comment on the allegations about Dowler, but Brooks said News International would cooperate fully with police, as well as conducting its own internal inquiries.

The Dowlers' lawyer, Mark Lewis, said they would sue the tabloid for its "despicable" behaviour and called for Brooks to quit.

Brooks maintained it was "inconceivable" that she had known about the actions and said she would remain in her position.

In the first sign of a commercial backlash from the allegations, carmaker Ford announced that it was pulling its advertising from the News of the World.

In a rare moment of reflection, The Times newspaper, also owned by Rupert Murdoch's News International group, said in an editorial that if the claims were true then "there will not be a journalist in the country who, after the warranted anger, will not feel shamed and depressed."