Celebrity campaigners and victims of press intrusion, including Hugh Grant, Gerry McCann and Christopher Jefferies have been to the Houses of Parliament to launch a Hacked Off petition urging the government to act on recommendation in the Leveson Inquiry.
The petition from the Hacked Off campaign, calls on David Cameron, Nick Clegg and Ed Miliband to work together on implementing the recommendation in the report for a new regulator with "statutory underpinning."
It has already been signed by more than 10,000 people, who are calling for the politicians to "ignore pressure from media barons and introduce legally-backed regulation, independent of politicians and the press; place tighter limits on how much of our media an individual is allowed to own, and promote investigative journalism through effective public interest defences."
Launching the petition outside parliament were Christopher Jefferies, the landlord wrongly arrested for the murder of Joanna Yeates, Gerry McCann, father of missing Madeleine, and actor Hugh Grant.
McCann urged politicians to "do the right thing" and accept in full the suggestions for a new regulatory system.
"I think the only reason we went to Leveson was to affect change and if Leveson's report isn't implemented in full then I would say that giving evidence for all of the victims has been almost useless," he told the Press Association.
"For almost all the victims, the reason they were there was to stop other, ordinary people who were caught up in the most unfortunate circumstances suffering unnecessarily beyond what's happened to them.
"And I feel if Leveson is implemented we will be some way on that route.
"The jury will still be out of course, to it working in practice, but we will certainly be a few steps further forward."
He said he was not expecting an "immediate response suggesting it would be implemented in full", but said there was an onus on politicians.
"Our politicians have now got the ability to do the right thing, and the right thing is to implement in full," McCann said.
"And I think the MPs have an opportunity to redeem themselves a little bit with the public by accepting this, putting party political issues aside, and doing the right thing for everyone involved."
Earler, retired teacher Jefferies, told ITV News he would feel "let down" if the Prime Minister decided to side-step recommendations on legislation.
"I would certainly feel let down," he said. "I would think it would be a disaster.
"I was very struck by the fact that almost the first words that Lord Justice Leveson said when he gave his press conference were that this was the seventh report that has been issued in 70 years as a result of public concern about abuse of power by the press.
"Nothing has changed in those 70 years though this is, I think, the opportunity to make sure we're not in the position we have been recently, ever again."
Mr 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.
"I mean the Prime Minister makes a great show of saying that he agrees with very much of what is in Lord Justice Leveson's report but he thinks it can be achieved without legislation.
"Well, I've just explained why it seems to me that really will not work and is not good enough."