The Leveson report is now out and has backed statutory underpinning for an independent regulator. It has rejected the newspaper industry’s own proposals. So now the political process begins.

The Daily Express steps in with a “declaration of independence” on the freedom of the press applauding to Leveson for the PPC criticism but warning him against entering “very dangerous territory indeed” in his recommendation on a legislative eye on the press self-regulation.

The Guardian editorial on Leveson broadly welcomes the report and the Independent regulator with the assurances on public interest and legal costs – but it points out the political difficulties of getting legislation through and warns of ‘mission creep’ on the statutory backstop regulator, Ofcom.

The Telegraph says it supports the outline of an Independent regulator but without the statutory sanctions.

The Daily Mail says that Leveson is ‘playing with words’ and that statutory ‘underpinning’ is the same as bringing in a press law that could be used to restrict the newspapers. It says that the punishment for failing to join the ‘independent’ regulator would be pernicious.

Leveson has cast scarce light on the issue of media ownership, says Harold Evans, which comes as one of the biggest disappointments of the report.

The man who started this all (arguably) with his phone-hacking investigation, Nick Davies, says that he has no problem with Leveson’s report.

Steve Richards of the Independent argues that Leveson has got the balance right but that Cameron is running a political risk in trying to juggle his libertarian instincts and the desire to reform the press.

Fraser Nelson of the Spectator takes to the Telegraph to hail David Cameron for taking an historic stand that might preserve the press from government control – a freedom enjoyed since 1695, he says.

Rafael Behr of the Statesman defends Ed Miliband’s stance in favour of statutory regulation, but says that the whole process is like sorting out ‘a museum’.

In a detailed article the Financial Times declares that it has ‘reservations’ about Leveson’s plan for an independent regulator.

The Independent’s John Rentoul says that Leveson contradicts himself – he says it’s not state regulation but it is regulation by statute.

As Gary Gibbon points out, Leveson has made it tough for David Cameron to reject statutory regulation

LSE’s Damian Tambini argues that the most important part of the report is how it deals with the ‘Desmond’ problem. How do you incentivise papers to be part of a regulatory body. Is this statutory or not?

The New York Times opposes Leveson and says that all you need is criminal law to limit press freedom.

[If you are interested in the instant reactions of Polis director Charlie Beckett check out his tweets at @CharlieBeckett]