It comes on the eve of the sixth anniversary of the terror attack.
Detectives are believed to be contacting a small number of the 52 families, The Daily Telegraph reported.
Meanwhile, motor giant Ford said it was suspending advertising with the News of the World following allegations the paper hacked the mobile phone of murdered schoolgirl Milly Dowler.
The announcement came as a further blow for News International chief executive Rebekah Brooks, who pledged her “full co-operation” with the police inquiry into the claims, which date to her time as the paper’s editor.
A spokesman for the car-maker said Ford was “a company which cares about the standards of behaviour of its own people and those it deals with externally”.
Two other companies, Npower and Halifax, confirmed they were also considering whether to continue advertising with the paper amid a rising tide of anger at its alleged conduct.
As politicians from across the political spectrum vented their fury, Ms Brooks said she was “sickened” by the allegations and promised the “strongest possible action” against those responsible.
She insisted she had known nothing of the alleged actions of a private investigator working for the paper and made clear she had no intention of standing down from News International.
Her comments however did little to assuage the growing chorus of demands for her to consider her position and for a full-scale public inquiry into the conduct of the press and the way that it is regulated.
The pressure intensified with the confirmation by police that the parents of murdered Soham schoolgirls, Holly Wells and Jessica Chapman, had also been contacted by officers on the hacking inquiry. The condemnation was led by David Cameron who described allegations that a private detective hacked into 13-year-old Milly’s voicemail messages while police were still trying to find her as “really appalling”.
“If they are true, this is a truly dreadful act and a truly dreadful situation. What I have read in the papers is quite, quite shocking.”
Home Secretary Theresa May said the alleged behaviour was “disgusting”, adding: “The mindset of somebody who thinks it’s appropriate to do that is totally sick.”
Labour leader Ed Miliband said there should be a public inquiry once the police investigation was complete and he called on Ms Brooks to “examine her conscience” and consider her position.
“This is a stain on the character of British journalism,” he said.
“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.”
Meanwhile the Press Complaints Commission — the industry’s own watchdog — accused the News of the World of “lying” during an earlier investigation which it conducted into the allegations.
“I am the regulator but there is only so much we can do when people are lying to us,” PCC chairman Baroness Buscombe told the BBC’s Daily Politics programme. “We know now that I was not being given the truth by the News of the World.”
In the Commons, Labour MP Chris Bryant — who believes his phone was hacked by the News of the World — employed a little- used procedural device to win a three-hour emergency debate on the issue to be held tomorrow.
Downing Street insisted that the “absolute priority” had to be the ongoing Metropolitan police investigation, codenamed Operation Weeting.
Deputy Prime Minister Nick Clegg did not rule out ministers ordering a public inquiry at a future date.
The latest row erupted after The Guardian reported that private detective Glenn Mulcaire — who was subsequently jailed for plotting to hack into the phones of royal aides — hacked into Milly’s mobile phone following her disappearance in 2002.
When the inbox was full, he was said to have deleted messages so that more could be recorded, giving her distraught family false hope that she was still alive and using the phone.
In a message to News International staff, Ms Brooks said that she had written to Milly’s parents, Bob and Sally Dowler, to assure them that News International would “vigorously” investigate what had happened.
“It is almost too horrific to believe that a professional journalist or even a freelance inquiry agent working on behalf of a member of the News of the World staff could behave in this way,” she said.
“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 that you all realise it is inconceivable that I knew or worse, sanctioned these appalling allegations.”
She said that she was aware of “the speculation about my position”, but stressed: “I am determined to lead the company to ensure we do the right thing and resolve these serious issues.”
However solicitor Mark Lewis, for the Dowlers, said they would not be impressed by her remarks.
“Ultimately, if she didn’t know what as happening, then what was she doing as editor. She has risen in the company very high, so it is either she should resign because of incompetence or she should resign because she did know what was (going on) and therefore it is just not right to carry on doing that job.”
In a statement to The Guardian, Mr Mulcaire apologised for the “hurt” his actions had caused, and insisted he had not intended to interfere with a police investigation.
“I want to apologise to anybody who was hurt or upset by what I have done. I’ve been to court. I’ve pleaded guilty. And I’ve gone to prison and been punished. I still face the possibility of further criminal prosecution,” 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.”