Lord Justice Leveson's plans to introduce a statutory role for newspaper regulation caused a split in his inquiry team and could give crucial backing to David Cameron's defence of a free press, it emerged last night.

A prominent member of Lord Justice Leveson's panel, the Liberty director Shami Chakrabarti, is siding with the Prime Minister and against the judge over the degree of statutory involvement needed for new independent regulation – the intractable issue which is dividing Parliament, the media and victims of press intrusion.

Lord Justice Leveson held talks with Ms Chakrabarti to try to persuade her to agree with

the rest of the inquiry team, The Independent on Sunday understands, but failed to secure her full backing.

Ms Chakrabarti's views emerged yesterday, effectively throwing a lifeline to Mr Cameron, who is at odds with not only Lord Justice Leveson but with the Deputy Prime Minister, Nick Clegg, most members of Parliament and the families of Milly Dowler and Madeleine McCann, and other press victims.

A petition calling for the UK's three main party leaders to bring in a new press watchdog backed by law had attracted more than 56,000 signatures last night, little more than 24 hours after its launch on Friday.

Mr Cameron has insisted he does not want to "cross the Rubicon" of allowing any statutory role on regulation, including passing legislation which establishes the new measures in law, and allowing Ofcom, the broadcasting watchdog which reports to ministers, a supervisory role over the "independent" regulator. There are also concerns about enshrining in law incentives to encourage newspapers to join a new regulator and scrapping exemptions for public interest journalism under the Data Protection Act.

It is even possible, say legal sources, that newspapers could use the European Court of Human Rights to complain that their freedoms are being infringed by full-blown statutory regulation.

Fraught talks over how to reach agreement on Lord Justice Leveson's recommendations will continue tomorrow. Ed Miliband and David Cameron, who held "robust" exchanges in their first meeting alongside Nick Clegg last Thursday, are to temporarily step back from cross-party talks to take the heat out of the discussions. Instead, Maria Miller, the Culture Secretary, and her Labour shadow, Harriet Harman, will join Simon Hughes for the Lib Dems in trying to reach agreement. Mr Cameron will also attend talks chaired by Ms Miller with newspaper editors about a way forward, Downing Street announced last night. There are differences of opinion among editors about the shape of the regulator, and the Prime Minister's intervention underscores the urgency of reaching consensus among newspapers.

A source close to Mr Miliband, the Labour leader, stepped up pressure on the Prime Minister, saying he needed to "show the strength to do the right thing". "He is not only defying the judge that he appointed, and the families whom he said he would never let down, and the whole of Parliament. This is a big moment for Cameron. He needs to show leadership and strength that is required to stand up for the public interest in the face of very powerful vested interests."

There are between 40 and 70 Tory MPs siding with the majority of Labour and Liberal Democrat MPs in wanting to see the Leveson report recommendations implemented in full, including statutory underpinning of a new regulator. Mr Cameron has the backing of the majority of newspapers and most Conservative members of his Cabinet, as well as a substantial number of Tory MPs.

Madeleine McCann's father, Gerry, and the author JK Rowling, are among the victims of press intrusion to put pressure on Mr Cameron to change his mind about statutory regulation.

Yet in a crucial intervention that could change the nature of the battle, Ms Chakrabarti, a member of the six-strong panel of assessors, wrote in The Independent yesterday: "The Prime Minister is right to be concerned about any Government-appointed body 'supervising' the independent regulator. That would bring about the danger of political control by the back door. It is unnecessary and must be resisted. Furthermore, the report contains a last-ditch alternative of compulsory statutory regulation, should the press be unwilling to implement his proposed scheme. Again, the Prime Minister is right to reject this unacceptable plan B, which Liberty would be unable to support."

On the opening session of his inquiry in July last year, the judge said that he would "strive for unanimity". But while she backs the judge in the general thrust of the report, Ms Chakrabarti opposes him over a key principle of how to deliver the necessary incentives for newspapers to join a new independent regulator.

Ms Chakrabarti's dissent is buried in the small print of the Leveson report. On page 1,775, where the judge recommends that Ofcom, which is a statutory body and reports to ministers, is given new powers to oversee a new press regulator, a footnote reveals that the Liberty director is opposed to this key principle – seen inside No 10 as one of the key "Rubicon", or red-line, issues.

The footnote reads: "Shami Chakrabarti has advised that she prefers this role to be fulfilled by the court but I do not see how the court, of its own motion, could adopt an adjudicative role in relation to certification or subsequent review."

Ms Miller and Mr Cameron are to use the talks with editors to urge them to reach agreement to show that statutory intervention is not necessary.

The Government will publish a draft Bill, which the Culture Secretary has said will be used to demonstrate that legislation will be detailed and lengthy. But Labour sources said that in Ireland, tougher press regulation was contained in just two clauses in a defamation Bill.

Why do we cross the Rubicon?

The phrase "crossing the Rubicon", used by David Cameron in the Leveson debate, means to take an irrevocable step in one direction, and can be traced back to 49BC when Julius Caesar and his 50,000-strong army crossed the river of the same name on their way to Rome, effectively ushering in the Roman Empire.

An ancient law meant that any general who crossed the Rubicon River, to enter the Roman Republic with an army, would be committing treason. If he did so, he would be stripped of command and prosecuted. Caesar, although hesitating, did cross, with his troops by his side. Aware that he must either conquer Rome or die, he famously said: "Alea iacta est" ("the die has been cast").

Doubts linger over which river is the historical Rubicon, but it is thought to be the river flowing through Savignano, Italy. The town was renamed Savignano sul Rubicone by Benito Mussolini.