Ex-Deputy Prime Minister Lord Prescott, actor Hugh Grant and dozens of other public figures are demanding an inquiry into newspaper phone-hacking.
It follows allegations that a private investigator working for the News of the World hacked into Milly Dowler's phone.
Mr Grant said people felt "viscerally sickened" by the revelations.
The House of Commons is to debate the calls for an inquiry for up to three hours on Wednesday.
News International, which owns the News of the World, has promised to investigate the claims made against it.
Hacked Off, a campaign supported by Mr Grant, Lord Prescott, Conservative former Health Secretary Lord Fowler, Labour MP Chris Bryant, Liberal Democrat MP Adrian Sanders and the Dowlers' lawyer, Mark Lewis, has started an online petition calling for a full public inquiry.
Police are already investigating allegations over phone-hacking by detectives working for the News of the World, but the group described this as too "narrowly focused".
In a statement, Hacked Off said: "Even if there are prosecutions, they will concern themselves only with specific cases and individuals. Without an inquiry most of the evidence will stay secret and the wider story of illegal information-gathering and the official response to it will never be told."
Thirteen-year-old Milly went missing in March 2002 and her body was discovered six months later. Nightclub bouncer Levi Bellfield was convicted of her murder last month.
The Guardian claims that Milly's voicemail was hacked into after she disappeared and that messages which had already been listened to were deleted, to make room for more to be left.
Lawyers acting for the Dowler family argue this could have led relatives to hold "false hope" that the teenager was still alive, increasing their eventual agony.
Mr Grant, who carried out an undercover investigation on hacking for the New Statesman magazine in April, told BBC Radio 4's World at One: "It's been hard to get people to viscerally feel sickened and outraged and 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."
Mr Grant was also asked if he thought it was appropriate for Rebekah Brooks, editor of the News of the World at the time of the alleged hacking of Milly's phone, to lead the internal investigation into hacking for the newspaper's parent company News International, where she is now chief executive.
He replied: "That would be like asking me if I thought Hitler was a good person to clear up the Nazi Party. It's completely absurd."
Mr Grant said claims by Mrs Brooks and another former editor, Andy Coulson, that they had been unaware of hacking while they were in charge at the News of the World "makes either him and Rebekah Wade the worst editors in the history of journalism or liars".
In the House of Lords, Lord Fowler called for an inquiry once the police investigation is over.
He said: "My view of the press is that newspapers are there to expose stories of injustice and abuses of power, not to interfere with the private lives of the public."
Lord Fowler added: "Today's revelations about Milly Dowler are almost beyond belief, and certainly beyond contempt... This is not a matter of party politics, but protecting the public."
Lord Prescott told peers the allegations were "the latest and most serious" made against News International and that such "criminal acts" had to be dealt with more thoroughly.
For the government, Baroness Browning said: "We must await the outcome of the police investigation. If these allegations are found to be true, there will need to be new avenues to explore."
In a statement to News International staff, Mrs Brooks said: "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.
"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."