David Cameron said that the alleged hacking of Milly Dowler's phone was a 'truly dreadful act' (Image: BBC)

Prime Minister David Cameron said today that he was shocked by revelations that the News of the World may have hacked into the phone of the murdered schoolgirl Milly Dowler, describing the alleged interceptions as "truly dreadful".

Speaking for the first time since the hacking story broke, Cameron echoed statements made by other senior British politicians, according to The Guardian. The prime minister called for police to undertake a "vigorous" investigation into the allegations.

"On the question of the really appalling allegations about the telephone of Milly Dowler, if they are true, this is a truly dreadful act and a truly dreadful situation," Cameron told reporters at a press conference in Afghanistan.

"What I've read in the papers is quite shocking, that someone could do this knowing that the police were trying to find this person and find out what happened."

The outcry began on Monday night after The Guardian reported that News of the World journalists hired private investigators to hack into Milly Dowler's phone shortly after the 13-year-old went missing in March 2002.

It is alleged that the journalists deleted messages from her voicemail inbox when it became full, interfering with the police investigation and fuelling the Dowler family's hopes that she might still have been alive. The decomposed remains of Milly's body were discovered six months after her disappearance.

Key Murdoch lieutenant intends to stay put, despite mounting pressure

Rebekah Brooks, now the chief executive of News International, does not intend to resign (Image: Getty)

The News of the World's editor at the time was Rebekah Brooks, now the chief executive of the paper's parent company News International - which is in turn owned by the global media conglomerate News Corporation.

Confirming an earlier report by the BBC's business editor Robert Peston, Brooks pleaded ignorance in a statement to News International staff, denying that she knew about the alleged hacking of Milly Dowler's mobile phone or about any other instances of phone hacking under her watch.

"I hope that you all realise it is inconceivable that I knew or worse, sanctioned these appalling allegations," she said.

Brooks said that she would not step down, adding that she was "determined to lead the company to ensure we do the right thing and resolve these serious issues".

But Labour's leader Ed Miliband added to the pressure on Brooks today, stating that she ought to "consider her conscience and consider her position" in light of what is alleged to have taken place under her editorship.

Brooks' successor as the News of the World's editor, Andy Coulson, resigned from the position in 2007 after the tabloid's royal editor was found to have hacked into the voicemail messages of royal household members.

Coulson then quit his post as David Cameron's director of communications at the start of this year, claiming that ongoing questions about phone hacking during his tenure were proving to be a distraction for Downing Street.

Coulson has always denied being aware of illegal activities during his time at the helm, but may again come under pressure to explain whether he was aware of the News of the World's alleged activities on the Milly Dowler story. He was Brooks' deputy editor at the time of the disappearance and murder.

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