David Cameron must ignore some of his Tory colleagues and listen to Lord Justice Leveson when the judge outlines reforms to the regulation of the press, the deputy leader of the Liberal Democrats has said.

In the wake of a Times report on Friday that the prime minister is planning to give the industry another chance to improve self-regulation, Simon Hughes said that a series of scandals had shown this system has failed.

Hughes, who received damages from News International earlier this year after his phoned was hacked by the News of the World, said: "David Cameron would do well to ignore the calls from some in his party who for far too long have been far too close to media owners and instead listen to the judge that he appointed to look into these matters in detail. After everything we know now, the public will simply not accept the failure of this government to finally sort out this issue, which successive governments have failed to sort out before."

The Lib Dem deputy leader, who accused the News of the World of "criminal behaviour on an industrial scale" when he settled his civil case in the high court earlier this year, spoke out after the Times reported that Cameron is preparing to reject statutory intervention in the regulation of the press.

Sources have confirmed that the prime minister "broadly" believes the industry should be give another chance to improve self-regulation by making further concessions to show that the new system is genuinely independent and, critically, with editors banned from being involved in adjudications on complaints.

However, this does not have the support of the Lib Dems, who believe self-regulation has failed.

Hughes said the state should never regulate the content of newspapers but that new systems needed to be put in place to guard against repeat lapses in standards in the press, such as the phone-hacking scandal.

"The scandals which have been hugely damaging to the press in our country should demonstrate beyond any reasonable doubt that the system of self-regulation has failed," he added. "Nobody is arguing that the state should ever regulate the content of newspapers but there is a strong case for a new system which will require newspapers to have the systems in place which will prevent widespread criminal behaviour and unacceptable breaches of privacy from happening again."

Cameron told Leveson during his testimony that the future press watchdog "can't be self-regulation, it has to be independent regulation". But he strongly hinted he did not support full statutory regulation.

"It would be much better if we could deliver it without statute," he said, adding that the test of the new press regulator would be whether it worked for people like the parents of Milly Dowler and Madeleine McCann.

"The test of a regulatory system is not: does that make the politicians happier? The test of the system is: is it going to provide proper protection to ordinary families who, through no fault of their own, get caught up in these media maelstroms and get completely mistreated?" he said.

Lord Black, the chairman of Presbof, which funds the discredited Press Complaints Commission, is believed to be playing a pivotal behind-the-scenes role. He is also a former PCC director.

He is close to Cameron and is co-ordinating the industry's response to Leveson, including proposed new powers of investigation and fines of up to £1m for breaches of strict codes of conduct on a range of issues from privacy to accuracy.

"Statutory regulation of the written word would be an unacceptable impingement on press freedom," Black said in his submission to the inquiry. He told Leveson during oral evidence that any attempt to introduce new laws to govern newspapers would run the risk of getting "stuck in parliamentary aspic".

Black also warned that a statutory system would face "constant legal challenge to the legal decisions of a regulator" by newspapers.

The prime minister made clear in his evidence to the Leveson inquiry that he was wary of statutory regulation when he spoke of the dangers of "excessive" regulation.

In his statement to the inquiry, he said: "In my view, more effective regulation, independent of government, is a better option. I do not believe that direct regulation by the government or a government-appointed body would be appropriate as it would damage our democracy, inhibit a free press and indeed, it could erode the benefits of the media holding politicians to account and uncovering wrongdoing amongst politicians."

The behind-the-scenes machinations come at a sensitive time. Leveson is still working on his final report and recommendations and nobody wants to be seen publicaly to pre-empt this.

He has already expressed his "disappointment" that a confidential letter he sent to newspaper groups warning of potential criticism in his final report is being discussed by the press.

He made his disapproval known after Chris Blackhurst, the editor of the Independent, went on Radio 4's The Media Show on Wednesday and claimed that Leveson was "loading a gun" for the newspaper industry and that his warning letter, which was sent to all main newspaper groups, was a "point by point demolition" of the press.

Blackhurst said that Leveson was throwing the book at the industry and had failed to acknowledge that newspapers, not others, had uncovered scandal after scandal.

His remarks prompted the Leveson inquiry to issue a statement on Wednesday pointing out it was legally obliged under inquiries legislation to give anyone who will be criticised in his final report written warning of that potential criticism to give them an opportunity to respond to it.

The statement also said comments on his letter were a "misrepresentation" of the facts and that by their nature such letters were one-sided.

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