A group representing phone-hacking victims has branded negotiations between the press and No 10 a "pantomime", a "cosy stitch-up" and a "shady deal".
Hacked Off called for politicians across the spectrum to reject the current discussions on how to implement the Leveson Report during a press conference in Westminster on Monday.
Hacked Off is demanding greater statutory regulation of the press after Leveson
The organisation rejected the idea of a royal charter creating the new press watchdog - a solution the prime minister is said to be looking at, according to reports - and reiterated its support for statutory underpinning.
Professor Brian Cathcart, director of Hacked Off, said: "We express our dismay at the pantomime of ministers rummaging in the constitutional cupboard for medieval precedents with which to confer legitimacy on what they are doing.
"It is not clear what the detail is, but on the basis of our legal advice, a royal charter will provide barely comparable protection to the public to what they have today.
"And that, as Lord Justice Leveson and indeed everybody else has agreed, is grossly insufficient."
Prof Cathcart also attacked the "current disgraceful process where press regulation is being arranged behind closed doors by ministers and editors without due regard for the protection of the interests of the public".
Earlier this month the editors of national newspapers were summoned to Downing Street to meet the prime minister and discuss how to implement the recommendations of the Leveson Inquiry.
At Monday's press conference, victims of phone hacking queued up to attack the current process of negotiations and accuse the prime minister of reneging on his word.
They suggested it was unsuitable for the press - heavily criticised by Lord Justice Leveson - to play such a central role in negotiations about their own future.
Former Crimewatch presenter Jacqui Hames, who appeared at the Leveson Inquiry, accused David Cameron of breaking his promise to the victims of hacking.
Addressing Mr Cameron, she said: "From the point of view of the victims, your advisers at No 10 are giving every indication that you are preparing a cosy stitch-up with the newspaper editors and owners.
"A clear attempt is being made to sideline and ignore us, the victims, the people you said have been thrown to the wolves by press abuse."
Broadcaster Anne Diamond, who also gave evidence of press intrusion at the Leveson Inquiry, said the experience had been "stomach-churningly nerve-racking" and warned that the inquiry may become a "waste of money" if real action is not taken.
The culture secretary's role in implementing Leveson has also come in for criticism
Actor Hugh Grant, who sits on Hacked Off's board of directors, said it was "frankly sickening" that politicians had broken their promises to victims of press intrusion.
Grant insisted he would continue to campaign for meaningful regulation right up to the 2015 election if necessary.
He said: "This is a cause that I have every reason to believe will be won, and therefore I personally have no intention of easing up or giving up."
Prof Cathcart also commented on the role of culture secretary Maria Miller in implementing the Leveson report,
He questioned whether a minister who is "vulnerable" to the press should act on behalf of the public in negotiations on newspaper regulation.
Last week the Telegraph reported how they were contacted by Mrs Miller's special adviser and reminded of her involvement in Leveson meetings as the paper pursued an investigation into the culture secretary's expenses.
Prof Cathcart said: "What it illustrates very clearly is the risk - of which Lord Justice Leveson was so careful to try and avoid - the risk of politicians meddling in press regulation.
"If we have a process in which a minister is sitting down with editors and trying to work out what the future is, and that minister is vulnerable to the sorts of things that we have referred to, then how can the public have confidence that the outcome is for their benefit, rather than for the benefit of the politician or for the benefit of the editors.
"How can we trust a process in which ministers who claim to be acting for the public here are so vulnerable?"
When asked whether Mrs Miller should step aside from negotiations with the press, Prof Cathcart said: "We think that all ministers should step aside.
"We think that there should be a genuine cross-party process as envisioned by Lord Justice Leveson which would see through the essential, simple, modest legislation that is required to set up the recognition body which will protect the public interest so that we know that there isn't another PCC down the line."
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