The parents of murdered Soham girls Holly Wells and Jessica Chapman have been visited by police investigating phone-hacking by journalists.
Private investigator Glenn Mulcaire, working for the News of the World, allegedly hacked the phone of murdered girl Milly Dowler when she was missing.
News International has promised the "strongest possible action" if it is proven Milly's phone was hacked.
In a statement, Mulcaire apologised to anyone "hurt or upset" by his actions.
Jessica and Holly, both 10, of Soham, Cambridgeshire, were murdered in 2002 by school caretaker Ian Huntley, who was jailed for life.
BBC business editor Robert Peston says police are investigating whether the phone of Jessica's father, Leslie Chapman, was hacked by the press.
Our correspondent says that, in relation to the phone-hacking claims involving Milly, News International executives privately say they accept that the basic allegations are true.
"Perhaps more striking, however," he adds, "is that those executives also say that there may be even more embarrassing revelations to come about the way that News of the World journalists obtained information about other individuals."
Our correspondent told the BBC's Ten O'Clock News that News International has passed e-mails to police which appeared to show that the former editor of the News of the World, Andy Coulson, authorised payments to police for information.
He said he had tried to put the allegations to Andy Coulson but had received no immediate response.
Milly Dowler, who was 13, 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.
The Guardian has claimed Mulcaire intercepted messages left by relatives for Milly while she was missing and that the News of the World (NoW) deleted some messages it had already listened to in order to make space for more to be left.
In a statement released to the Guardian on Tuesday, Mulcaire made no direct reference to those allegations but apologised "to anybody who was hurt or upset by what I have done".
He said: "Working for the News of the World was never easy. There was relentless pressure. There was a constant demand for results.
"I knew what we did pushed the limits ethically. But, at the time, I didn't understand that I had broken the law at all."
He added that he "never had any intention of interfering with any police inquiry into any crime".
BBC Newsnight has learned that police investigating press phone-hacking have also spoken to Jacqui Hames, a former Met officer and presenter on BBC's Crimewatch, and Clarence Mitchell, spokesman for the family of missing child Madeleine McCann.
Mr Mitchell told the BBC that someone had tried to persuade his mobile phone network operator to reveal confidential information about his account.
Graham Foulkes, whose son died in the 7/7 bombings, has told the BBC he was contacted by police on Tuesday after his details were found on a list as part of the police investigation in hacking claims.
Meanwhile, Channel 4 News has reported that Dave Cook, a Metropolitan Police detective, was put under surveillance by News of the World journalists.
In a memo to staff on Tuesday, Rebekah Brooks, chief executive of NoW publisher News International, said the allegations Milly's phone was hacked were "almost too horrific to believe".
"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 added: "I hope that you all realise it is inconceivable that I knew - or worse - sanctioned these appalling allegations."
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 there should be "a proper inquiry into the culture and practices which allowed these things to happen".
Motor company Ford has announced a halt on advertising in the News of the World, pending the newspaper's investigation and response over the phone-hacking claims.
"Ford is a company which cares about the standards of behaviour of its own people and those it deals with externally," it said in a statement.
Energy company Npower and the Halifax bank have announced they are considering their options regarding advertising in the News of the World.
MPs will hold an emergency debate on Wednesday on whether there should be a public inquiry into the phone-hacking scandal.
House of Commons Speaker John Bercow granted the urgent debate 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.
Also on Wednesday, the Media Standards Trust - which aims to promote high news standards within the media - will launch the Hacked Off campaign calling for a public inquiry into "phone hacking and other forms of illegal intrusion by the press".
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.
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.