Pressure is growing on News International with Labour calling for an independent inquiry into journalistic practices at the News of the World over the hacking of Milly Dowler's phone.
The shadow home secretary, Yvette Cooper, called the newspaper's actions "despicable" and said there should be a wide-ranging inquiry.
The call comes amid reports that police are to meet with News of the World executives to discuss the hacking.
"Everyone across the country will be deeply disturbed and horrified at this shocking news," Cooper said. "The idea that private investigators working for a newspaper would hack into the phone of a missing 13-year-old girl is truly despicable."
Labour MP Tom Watson called on Monday for the prime minister to act over the phone hacking, but also laid some of the blame on his own party leader.
"Surely now we should hear from David Cameron and Ed Miliband," Watson said. "It's utterly disgraceful that they've let this scandal run on for as long as it has. No more cowardice – we want action."
Miliband later said he was "shocked by the news of the hacking of Milly Dowler's phone".
He added: "It beggars belief that anyone would undertake such a cruel and immoral act.
"The police inquiry must get to the bottom of who was responsible for this and who was complicit in it."
David Cameron, who was in Afghanistan on Monday, has yet to speak on the issue.
The BBC reported that police are to meet News of the World executives to discuss the phone hacking, although the Metropolitan police would not confirm the news on Tuesday morning.
Detectives from Scotland Yard's new inquiry into phone hacking, Operation Weeting, are believed to have found evidence of the targeting of the Dowlers in a collection of 11,000 pages of notes kept by Glenn Mulcaire, the private investigator jailed for phone hacking on behalf of the News of the World.
In the last four weeks Met officers have approached Surrey police and taken formal statements from some of those involved in the original inquiry, who were concerned about how News of the World journalists intercepted – and deleted – the voicemail messages of Milly Dowler.
The messages were deleted by journalists in the first few days after Milly's disappearance to free up space for more messages. As a result friends and relatives of Milly concluded wrongly that she might still be alive [see footnote]. Police also feared evidence may have been destroyed.
• The following was published on 12 December 2011 in the corrections and clarifications column: An article about the investigation into the abduction and death of Milly Dowler (News of the World hacked Milly Dowler's phone during police hunt, 5 July, page 1) stated that voicemail "messages were deleted by [NoW] journalists in the first few days after Milly's disappearance in order to free up space for more messages. As a result friends and relatives of Milly concluded wrongly that she might still be alive." Since this story was published new evidence – as reported in the Guardian of 10 December – has led the Metropolitan police to believe that this was unlikely to have been correct and that while the News of the World hacked Milly Dowler's phone the newspaper is unlikely to have been responsible for the deletion of a set of voicemails from the phone that caused her parents to have false hopes that she was alive, according to a Metropolitan police statement made to the Leveson inquiry on 12 December.