Media playback is unsupported on your device Media caption News International's Simon Greenberg said the company was "shocked and appalled"

News International boss Rebekah Brooks has promised the "strongest possible action" if claims that the phone of Milly Dowler was hacked are proven.

It is alleged a private investigator working for the News of the World hacked into the voicemail of the murdered girl while she was missing.

In a memo to staff, Mrs Brooks called it "almost too horrific to believe".

MPs will hold an emergency debate on Wednesday on whether to hold a public inquiry into the phone-hacking scandal.

"I have to tell you that I am sickened that these events are alleged to have happened," Mrs Brooks wrote.

"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."

She said that she had written to the Dowler family to assure them that the media group, which publishes the News of the World, would "vigorously pursue the truth and that they will be the first to be informed of the outcome of our investigation".

Her statement to News International staff added: "I hope that you all realise it is inconceivable that I knew - or worse - sanctioned these appalling allegations."

The Guardian claims private investigator Glenn Mulcaire intercepted messages left by relatives for 13-year-old Milly while she was missing in 2002, and that the NoW deleted some messages it had already listened to in order to make space for more to be left.

Image caption Schoolgirl Milly Dowler's remains were found six months after she went missing in March 2002

Labour leader Ed Miliband said the public would be "horrified that the grieving parents of an abducted child were made to go through further torture that somehow she was alive because her voicemails were being retrieved or deleted".

He called the allegations a "stain on the character of British journalism", adding: "The culture and practice of some parts of the industry bring into question the rest of the industry and that's why we need a proper inquiry into the culture and practices which allowed these things to happen."

House of Commons Speaker John Bercow granted the urgent debate on the possibility of a public inquiry following a call by Labour MP Chris Bryant, who accused the News of the World of "playing God with a family's emotions".

In the upper house, former Conservative Party Chairman Lord Fowler said an inquiry was needed in the wake of "one of the biggest scandals affecting the press in living memory".

Home Office minister Baroness Browning said the government would await the outcome of the police investigation before deciding whether further action was necessary.

Sir David Bell, who chairs the Media Standards Trust, which aims to promote high news standards within the media, said: "We've argued for years now that this is an iceberg and we've only seen the tip of it."

The trust is organising the Hacked Off campaign, which will be launched on Wednesday, calling for a public inquiry into "phone hacking and other forms of illegal intrusion by the press".

We will face up to the mistakes and wrongdoing of the past Rebekah Brooks, News International Chief Executive Statement in full

On BBC Radio 4's World at One programme, actor Hugh Grant - who investigated hacking for the New Statesman in April - said that he hoped the latest allegations would bring about a public inquiry.

It had previously been difficult to get people to care about the hacking scandal - which involved celebrities and MPs having allegedly been targeted - because "most victims are rich", Mr Grant said.

"It's been hard to get people to viscerally feel sickened and outraged, but now that people fully realise just how repulsive these people are - and the lengths to which they'll go - hopefully there'll be more momentum in getting something done," he said.

Media playback is unsupported on your device Media caption Press Complaints Commission chairman Baroness Buscombe: "You must sense my anger in all of this"

The chairman of the Press Complaints Commission, Baroness Buscombe, defended the body's actions over the phone-hacking allegations.

She told BBC Two's Daily Politics she was angry that the PCC had been misled by the News of the World and added: "There's only so much we can do when people are lying to us."

The Metropolitan Police launched Operation Weeting in January this year after new phone-hacking claims emerged. The force has faced criticism for its initial inquiry in 2006 into phone-hacking at the paper.

That probe led to the convictions and imprisonment of Mulcaire and then News of the World royal editor Clive Goodman in 2007 for conspiracy to access phone messages left for members of the royal household.

A number of alleged phone-hacking victims have since reached out-of-court settlements with the newspaper.

Quite shocking - that someone could do this knowing the police were trying to find this person and trying to find out what had happened David Cameron, Prime minister

'Determined to lead'

Nick Davies, the Guardian special correspondent who wrote the latest story, told the BBC: "This is one of the very few episodes that happened when she [Rebekah Brooks] was editing the paper, and she's clearly going to have to answer some questions about what she knew about what was going on."

Mr Miliband said that Mrs Brooks should "examine her conscience" and consider her position, although he said the issue of phone-hacking at the News of the World went "beyond one individual".

In her statement, Mrs Brooks said she was aware of speculation about her position but that she was "determined to lead the company to ensure we do the right thing and resolve these serious issues".

"We will face up to the mistakes and wrongdoing of the past and we will do our utmost to see that justice is done and those culpable will be punished," she wrote.

Image caption Mrs Brooks said the company would "not tolerate such disgraceful behaviour"

Speaking during a visit to Afghanistan, Prime Minister David Cameron said the allegations were "quite shocking - that someone could do this, actually knowing that the police were trying to find this person and trying to find out what had happened".

He added: "If they are true, this is a truly dreadful act and a truly dreadful situation."

Milly Dowler went missing in March 2002 near her home in Walton-on-Thames, Surrey. Her remains were found in remote woodland at Yateley Heath in Hampshire six months later.

Nightclub doorman Levi Bellfield was convicted of the murder last month.