Gerry McCann, father of missing girl Madeleine, has said the "sick culture" that led to his family being accused of murdering their own daughter to pay off their mortgage still exists in the UK press.

McCann on Monday afternoon laid down the gauntlet to prime minister David Cameron, calling on him to deliver the promise he made during and after the Leveson inquiry to "protect the people who have been thrown to the wolves as we were".

McCann was taking part in a press conference organised by Hacked Off, the group campaigning for stricter press regulation, on the eve of the first publication of No 10's plans for a new regulator backed by royal charter.

Representatives of Hacked Off called the briefing following a meeting with Cameron on Monday morning and said they were "not encouraged" by what they heard, fearing the prime minister is about to water down proposals to tighten up regulation of the press.

They fear that Cameron is surrendering to press interests, noting that the editor of the Daily Mail and the editor of the Financial Times were leaving Downing Street as they arrived.

McCann said he was not reassured by what he believed to be "backsliding words from politicians" and warned that any dilution of promises to protect innocent people from abuses by the media would be like "surrendering to the press and saying the whole Leveson process was a waste of time".

He added that Cameron owed it to "victims" of press intrusion like him to put a system in place "to protect ordinary people from the devastating damage that the media can cause".

No family should have to endure what his did, McCann said, recalling how he and his wife had been "labelled as murderers without a shred of evidence", that newspapers had reported their daughter was dead "over and over again, with no evidence", and one newspaper even claimed "that we sold Madeleine into slavery in order to pay off our mortgage".

He said he believed "the sick culture" on some newspapers that led to this "has not changed", adding: "Three years later, I see little remorse, no contrition. Sections of the press are still in denial."

McCann said the minimum Cameron must do to ensure this never happens again is implement the Leveson proposals for press regulation reform.

In their meeting with Cameron, Hacked Off representatives said they received no assurances that their proposals for a new watchdog would offer the robust and independent regulation that Leveson recommended.

The prime minister is set to publish the Conservative party's full proposals, including plans for a royal charter to establish a new press regulator, on Tuesday afternoon.

Brian Cathcart, director of Hacked Off, said he was "surprised" to hear from Cameron that the press may have a role in the appointments process in relation to the new watchdog.

"The prime minister gave us no reassurances about the idea that this body would be appointed in an independent and transparent way," Cathcart added.

He said Hacked Off was given "no encouragement" about the statutory framework that would ensure a press regulatory, established by royal charter, would be free of interference from government ministers on the privy council.

"He didn't dispute press reports this morning that there was no statutory protection for the royal charter preventing it being amended," said Evan Harris, associate director of Hacked Off.

Deputy Labour leader Harriet Harman, who attended the Hacked Off press conference, said she believed that if Cameron did not deliver on the Leveson proposals, parliament would. She noted that he had "no mandate" to implement a watered-down press watchdog.

Lord McNally, leader of the Liberal Democrats in the House of Lords, said a tripartite solution was the only one. "If we are doing to get the this fish in the bowl, you have to have three-party agreement," he said.

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