A petition calling for the UK's three main party leaders to bring in a new press watchdog backed by law has attracted more than 80,000 signatures since being launched by high profile victims of media intrusion on Friday.
Gerry McCann, father of missing Madeleine, and Christopher Jefferies, the landlord wrongly arrested for the murder of Joanna Yeates, urged the public to back their online campaign after David Cameron indicated he planned to spike recommendations to introduce legislation.
Jefferies won substantial libel damages from eight newspapers following their coverage of his arrest in connection with the architect's disappearance in 2010. He was later released without charge.
He said he wanted to tell the Prime Minister he was "very much mistaken" over his approach to statutory underpinning of press regulation.
He added: "I think he should listen not only to the voices of those that have been the victims of the press, but that he should listen to the voices of the National Union of Journalists who are in favour of some sort of statutory underpinning of this regulation.
"And that he should listen to all those MPs who are of the same view. In fact, it is probably true to say that there is a majority in Parliament that is opposed to the point of view to which the Prime Minister has chosen to entertain."
The Prime Minister's position has been roundly welcomed by the industry but sparked fury among victims and campaigners, with Harry Potter author JK Rowling the latest to wade into the row saying she felt "duped and angry" by the Tory leader's stance.
However, with the petition, Cameron is under pressure to drop his opposition to a law backing up the new watchdog the press have been tasked with devising.
Cameron has told MPs he has "serious misgivings" about Lord Justice Leveson's recommendation for independent self-regulation of the press underpinned by law.
The coalition is split on the issue, with Nick Clegg backing the legal underpinning of press regulation.
Ed Miliband said Labour "unequivocally endorses" Leveson's proposal that any new regulatory body should be set out in statute.
On Saturday, Downing Street confirmed that Cameron will attend Culture Secretary Maria Miller's meeting with the newspaper industry's leading editors next week in an effort to urge the press to act on the Leveson Report and set up a new watchdog.
Miller will warn that the press it must not drag its feet when it comes to acting on Lord Justice Leveson's calls to devise an independent regulatory body.
On Friday, Miller said that the "principles" of the judge's blueprint could be met without statutory backing, and will use the meeting to reiterate that to Fleet Street.