News Of The World has been implicated over the phone hacking of families of 7/7 bombing victims.
A solicitor representing some of the relatives said one family had been contacted by police and told their phone may have been hacked in 2005.
New allegations have also emerged of payments to the police by the paper.
The tabloid's owners has confirmed it passed to the police e-mails which appear to show that payments were authorised by the then editor, Andy Coulson.
Graham Foulkes, whose son David died in the Edgware Road blast, revealed he was contacted by officers as part of the police inquiry in phone hacking claims.
Foulkes, of Oldham, Greater Manchester, told the BBC how his family had waited for a week after the 2005 attacks for news of David.
"My wife and I were kind of all over the place, we were chatting to friends on the phone, in a very personal and deeply emotional context – and the thought that somebody may have been listening to that just looking for a cheap headline is just horrendous."
Foulkes said he would like to meet News International's owner, Rupert Murdoch, to talk to him about "the power he has".
He added: "I certainly think that News International need to come clean, they need to accept their responsibility and their culpability, and they need to do the decent thing, but I suppose they won't."
In a statement, News International confirmed that it complied with police in their investigation by passing on information.
"As News International and News Group Newspapers has reiterated many times, full and continuing co-operation has been provided to the police since the current investigation started in January 2011,” the statement read.
"Well understood arrangements are in place to ensure that any material of importance to which they are entitled is provided to them. We cannot comment any further due to the ongoing investigations."
Coulson, who went on to work for David Cameron as director of communications at 10 Downing Street, has not commented on the latest phone hacking allegations against News of the World, although it has been reported he has told friends he suspects he is being used to deflect attention
from News International.
Coulson resigned from his government role in January, saying the phone-hacking scandal has made it hard to focus.
Rebekah Brooks, the chief executive of News International is under mounting pressure to resign, as she is alleged to have been privy to a string of phone hacking allegations against News of the World.
Following the disclosure of the emails, the Financial Times, in an editorial, called on Rupert Murdoch to end Rebekah Brooks's tenure.
The editorial describes the alleged actions as “Exhibiting a fundamental lack of human decency”
It reads: “Mr Murdoch must set aside personal loyalties and remove those executives with any involvement in the affair – whether through their role as editors or at a corporate level. That includes those responsible for handling the company’s response,” the editorial reads.
It continues: “For a start, Rebekah Brooks, the chief executive of News Corp’s UK operations, should go. Assuming the allegations are correct, as the editor of the News of the World when Ms Dowler’s phone was hacked, her position is untenable. Although she has pleaded ignorance, the final
responsibility was hers.”
Brooks has denied all knowledge of phone-hacking at the paper, and told staff yesterday she intends to continue as chief executive of News International, the Rupert Murdoch-controlled media empire which owns the News of the World.
News of the World is set to lose millions of pounds in advertising revenue over the phone hacking allegations.
MumsNet, the influential parenting website, has said that it is going to withdraw an advertising campaign from the News of the World.
And Ford also announced it was pulling advertising. Other major clients, such as npower and Halifax, T-Mobile and Orange may follow suit.
News of the World also came under siege last night amid claims the families of the Soham murder victims may have been targeted.
The families of Holly Wells and Jessica Champman, who were 10 years old when they were killed in Soham by school caretaker Ian Huntley in 2002, were visited by Scotland Yard officers several months ago as their phones may have been hacked, a police source said.
Police are focusing on the phone of Jessica's father, Leslie Chapman, which was believed to have been hacked by the press.
Ian Huntley was jailed for life over the murders.
The scandal gathered fresh momentum on Monday when it emerged private investigator Glenn Mulcaire, working for the paper, may have hacked into murdered 13-year-old Milly Dowler’s phone after she went missing.
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.
The Guardian has claimed Mulcaire intercepted messages left by relatives for Milly while she was missing and that the News of the World deleted some messages it had already listened to in order to make space for more to be left.
That messages were deleted led Milly’s distraught family members to believe she was still alive.
News International has promised the "strongest possible action" if it is proven Milly's phone was hacked.
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".
There were further claims last night News of the World staff may have hacked into the phone of Sara Payne, the mother of murdered Sarah, a schoolgirl who was murdered in 2000, despite campaigning alongside her for new child protection laws.
And the spokesman for Kate and Gerry McCann, parents of murdered Madeleine, confirmed he has spoken to officers investigating phone hacking by journalists.
The revelations sparked a fierce backlash. Car maker 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.
The disclosure of payments to the police by email over the 7/7 bombings, represents "a significant development".
The police inquiry into illicit techniques used by News of the World, is expected to filter into a wider political realm.
The BBC reports that Cameron will returned from Afghanistan to find himself "at the centre of the row about media ethics, the power of the Murdoch empire and his own judgement in hiring Andy Coulson".
House of Commons Speaker John Bercow has granted an urgent debate into whether there should be a public inquiry into the phone-hacking scandal.
This follows a call by Labour MP Chris Bryant, who accused the News of the World of "playing God with a family's emotions".
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".
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.
Brooks, who edited the News of the World between 2000 and 2003 and is now one of the UK’s most powerful women following her promotion to company chief executive, insisted it was “inconceivable” she could have known about or agreed to phone-hacking while in charge of the paper.
In an email to staff, she wrote: “If the allegations are proved to be true, then I can promise the strongest possible action will be taken as this company will not tolerate such disgraceful behaviour.
“I hope you all realise it is inconceivable that I knew or worse, sanctioned these appalling allegations.”
The Dowler family solicitor, Mark Lewis, said: “If she didn’t know what was happening, what was she doing as editor?”
A number of alleged phone-hacking victims have since reached out-of-court settlements with the newspaper.
