The newspaper industry has announced its own proposals for a Royal Charter to underpin a new system of self-regulation.
David Cameron has insisted a cross-party agreement for a new system of press regulation protects the principle of the free press.
Labour says this is just the sort of legal under-pinning they were looking for but the Conservatives say that no such press law will exist.
Lord Justice Leveson has rejected claims that a previously undisclosed relationship between two of the barristers in his inquiry into press freedom threatened the legitimacy of its subsequent report.
The judge has said today in a letter that there was "simply no room" for a "breach of confidence or other conspiracy" as a result of personal relations between Carine Patry Hoskins, the inquiry's junior counsel, and barrister David Sherborne.
The Government has tabled an amendment in the House of Lords to exclude "small-scale" blogs from a new scheme of press regulation.
The short amendment, put forward by Home Office minister Lord Taylor of Holbeach, is expected to be debated tonight when peers discuss additions to the Crime and Courts Bill that would allow for exemplary damages and the awarding of costs against publishers who choose not to join a new regulator.
Lord Taylor's amendment would add "a person who publishes a small-scale blog" to the list of people and organisations who will be exempted from the new regulatory regime.
The list already includes bodies such as the BBC, book publishers and people who produce business newsletters.
The Financial Times has become the latest newspaper to oppose the all-party endorsed press regulation proposals.
The newspaper said the proposed new regime, following the Leveson inquiry, is "unsatisfactory" under a headline of "a muddle may be as bad as a muzzle".
"Too many hours and too much money have been spent on a process which has delivered a deeply unsatisfactory result," it concluded.
David Cameron has made a colossal "strategic blunder" by withdrawing from talks on the creation of a new system of press regulation, former Liberal Democrat leader Paddy Ashdown has said.
In an interview with BBC Radio 4's The Week in Westminster, to be broadcast today, Ashdown said that Cameron has angered his own MPs, supporters in the media and his Lib Dem coalition partners.
"I have not seen an avoidable strategic blunder made by a British prime minister or indeed the leader of a British political party which matches that of Mr Cameron over Leveson," he said .
"He marched his troops up to the top of the hill and then he had to march them back down again.
"In terms of strategy, this seems to me to make the Grand Old Duke of York look like a military genius."
Mr Cameron broke off talks with Ed Miliband and Nick Clegg on the implementation of the Leveson report on press standards after the Labour and Lib Dem leaders insisted the planned new regulator should be reinforced by legislation.
The Daily Mirror political correspondent Tom McTague is reporting that Labour is trying to change the plans for press regulation to exempt blogs:
Labour table amendment to Royal Charter proposals due to be debated int the Lords on Mon. Means blogs etc to be exempt from watchdog remitFrom @MirrorMcTague on Twitter:
Lab's Leveson clause removes any site "written by one person.. where financial turnover .. is small or site not run primarily for profit.”From @MirrorMcTague on Twitter:
The Royal Charter clause also covers "small blogs.. edited with a series of contributors"From @MirrorMcTague on Twitter:
Philip Webster, editor of digital editions of The Times, said the newspaper had “very serious concerns” about the press regulation proposals.
“We have serious concerns, we are looking at those concerns," he told ITV News UK Editor Lucy Manning.
“We are worried about the proposals for exemplary damages, we’re worried about the proposals for apologies, we’re worried about the overall cost of the plan.
“But we have yet to decide what to do, we are in no hurry.”
Media mogul Rupert Murdoch has said it was “unlikely” that the Queen would sign the Royal Charter on press regulation.
UK Royal Charter requires Queen's signature. Unlikely without full all party support. Queen doesn't do politics.From @rupertmurdoch on Twitter:
But ITV News UK Editor Lucy Manning said it would be more political for the Queen to refuse to sign the charter because it is, in fact, backed across parties.
The Spectator magazine has announced that it will not sign up to the Royal Charter on press regulation.
Editor Fraser Nelson said: “Our view is that press regulation and the freedom of the press are too important to be decided by a deal cooked up between politicians and Hacked Off at 2am in Ed Miliband’s office.”
Alan Rusbridger, editor in chief of Guardian News & Media has said that he has "grave reservations" about proposed press regulation legislation relating to exemplary damages, but added that it has been a big improvement on existing regulation.
In a statement, Rusbridger said:
– Alan Rusbridger
We welcome the fact that there has been cross-party agreement. The regulatory settlement is by and large a fair one, with compromises on all sides.
We retain grave reservations about the proposed legislation on exemplary damages.
The agreed terms are not ideal, but after two years of inquiry and debate we finally have the prospect of a robust regulator that is independent of both press and politicians.
It's a big improvement on what went before.
Deputy Prime Minister Nick Clegg has urged Britain's leading newspapers to support the politically-endorsed press regulation deal and recognise its benefits.
"The whole design of Leveson was based on ... independent self-regulation, but with a number of incentives which make it worth newspapers actually joining in the system," he said.
The Liberal Democrat leader appealed for editors and other influential media figures to recognise the benefits of the proposed new regulatory system, saying:
– Nick Clegg
I hope that when they examine the fine print, they will see that the incentives are strong and that it's worthwhile, not least in order to restore public trust in the conduct of newspapers, for them to join in with the system, and I very much hope they will.