Hacked Off's online petition calling on the government to comply with the findings of the Leveson Inquiry has been signed by more than 100,000 people.
Hugh Grant, a member of Hacked Off, has called David Cameron's position on the findings of the Leveson Inquiry "very close to disgraceful".
He told The Andrew Marr Show of his "astonishment" at Cameron's "betrayal" by declaring there was no need for statutory underpinning.
Grant said reforms "simply won't work without it".
The petition urges David Cameron and Nick Clegg to, "implement, as soon as possible, the recommendations of the Leveson Report in full".
It urges the government "ignore pressure from media barons and introduce legally-backed regulation, independent of politicians and the press" and "place tighter limits on how much of our media an individual is allowed to own, and promote investigative journalism through effective public interest defences."
Gerry McCann and Christopher Jefferies launching the petition last Friday
Conservative MP John Whittingdale, who chairs the Commons Culture, Media and Sport Select Committee, said he believed people backed self-regulation rather than new laws, saying legislation could stifle free speech.
"As people come to think about this carefully, they will realise the dangers of going down this road," Whittingdale said.
"Everybody agrees there needs to be an independent body to regulate the press.
"The passing of legislation is only necessary if the press then demonstrate they will not accept the rulings of that body.
"It's up to the press to prove they will go along with it. If they don't, then there may need to be legislation."
He has also claimed Lord Justice Leveson's recommendations were "mild".
"We thought the report was intelligent and clever but at the mild end of what everyone hoped for.
"We thought the upside of it being mild was that there was no way the Prime Minister can't endorse this, this is something that can get through."
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.
Group director Brian Cathcart said the 100,000 landmark was "a powerful indication of the strength of public feeling on Leveson.
"We have long known that the public is firmly behind effective, independent regulation of the press, which is what the Leveson report recommends.
"We hope that the Prime Minister, who last Thursday appeared to reject a key part of the recommendations, is listening to the voice of the public, just as he promised he would in his evidence under oath at the Leveson Inquiry.
"He also promised to listen to the voices of people who have suffered from press abuses, and they have clearly stated their approval for the Leveson proposals."
The petition needed 100,000 signatures to be considered for a commons debate and comes ahead of the Prime Minister and Culture Secretary's meeting with newspaper editors next week, to discuss the future of press regulation and whether the industry can deliver it alone. Commons is meeting next week to formally debate the findings.
Suggested For You
SUBSCRIBE AND FOLLOW
Get top stories and blog posts emailed to me each day. Newsletters may offer personalized content or advertisements.Learn more