Seven inquiries in 70 years haven’t done much to improve Britain’s toxic tabloids. But Lord Justice Leveson is hoping the eighth — his blockbuster report released in Britain overnight — will do the trick.

In London yesterday, victims of Fleet Street’s red-tops welcomed his lordship’s call for a tough new independent press regulator, backed by the law. And a throng of MPs lined up to do the same. Experts everywhere on British TV called Leveson’s plans “clever”, “sensible”, “moderate”, “reasonable” and “proportionate”.

And then up popped Prime Minister David Cameron to make a statement to parliament. And the future suddenly became less clear. Cameron told a packed House of Commons that he and Lord Leveson agreed on just about all of the recommendations … except for one thing: the PM didn’t believe any new laws were needed.

That would be crossing the Rubicon, he said, and setting a dangerous precedent for the government to use laws to control the press. This was no more than had been expected of the PM, but it was a let down all the same.

Since Lord Leveson’s 2000-page report had just made it clear a new legal framework was “essential” for his proposals to work, Cameron’s putative veto was a major blow, only 90 minutes after the report’s release.

Of course, it’s conceivable the British PM will change his mind in coming weeks, as Labour leader Ed Milliband, Liberal-Democrat deputy PM Nick Clegg and scores of Conservative backbenchers try to persuade him that a new legal framework is vital. But if he refuses to budge, it will be extremely hard to get any new law through parliament, even if the majority of MPs want one, because the government controls the legislative agenda.

Hardcore supporters of tougher press regulation — like the Hacked Off campaign fronted by actor Hugh Grant — have warned legislation needs to be introduced in the session that begins in May 2013 to stand a chance of becoming law before the next election. Not surprisingly, they greeted the Leveson report yesterday by saying: “The press must be given a deadline. The inquiry is over. Now is the time for action.”

So what happens next? Could Leveson’s system of independent regulation work without legal underpinning, and what exactly does he have in mind?

To take the last first — and borrow from the Prime Minister’s handy summary — Leveson is proposing “an independent self-regulatory body, with a standards code, an arbitration service, and a speedy complaint-handling mechanism. Crucially it must have the power to demand up-front, prominent apologies and impose million-pound fines.”

Note the “prominent apologies” and “million-pound fines”. That sounds like a regulator that can bite.

Leveson says his arbitration service could deal with people whose privacy has been invaded or reputation damaged, but who don’t have the money to sue. If newspapers refuse to play ball they could then face exemplary damages in any subsequent court hearing, Leveson suggests.

So who would be running this regulator and dishing out punishment? Well, not the government and not the press, and not some new quango set up for the purpose. Its members would be independent, as would its chair, and the majority would have to be drawn from outside the media. Crucially, current editors, proprietors and politicians would not be allowed. Nor would the members be chosen by the government or the industry, although editors would be able to sit on the appointment panel.

Crucially, Leveson says it should be up to the press — and not the government — to design this system and make it work.

It’s very clever to call this “self-regulation” because it’s actually nothing of the sort. And it’s a smarter solution than almost anyone expected. But Leveson is adamant we can’t let the press continue to “mark its own homework”. And in that he has almost unanimous support from the British public and British politicians.

So, these are “the Leveson principles”, according to Cameron, “the central recommendations of the report”. He immediately told parliament:

“I accept these principles, and I hope the whole House will come behind them, and the onus should now be on the press to implement them and implement them radically.”

But in saying that, he is quietly passing the buck, because Leveson clearly believes none of this will be delivered unless the press has a gun to its head. That gun is the law. Without legal backing, legal oversight and the threat of statutory regulation, Leveson believes the press won’t clean itself up. He suggests the current media regulator, Ofcom, should be given the job of disciplining dissidents. Ofcom would, in Leveson’s view, also have a role in approving industry codes and monitoring the regulator’s performance.

In this, Leveson has found a clever variation on the old trick of threatening legal action to make the industry regulate itself. His version would keep the law there forever, as a backstop, so the incentive to behave well would remain after the hoo-hah dies down.

The other reason for having a legal framework, of course, is to give backing to the penalties and to pave the way for those exemplary damages he has in mind.

Strangely enough, one of those on TV yesterday, backing the need for legislative muscle, was Alastair Brett, who was until recently the top lawyer at Rupert Murdoch’s Times. He won’t be getting a Christmas card from his old boss.

Crikey won’t pretend to have read the entire 2000-page report, but there are a couple of passages that caught our eye. In his 56-page summary, Leveson has a swipe at the tabloids, saying:

“There have been too many times when, chasing the story, parts of the press have acted as if its own code, which it wrote, simply did not exist. This has caused real hardship and, on occasion, wreaked havoc with the lives of innocent people whose rights and liberties have been disdained.”

He goes on:

“There has been a recklessness in prioritising sensational stories, almost irrespective of the harm that the stories may cause and the rights of those who would be affected.”

Some of these people, like the parents of Milly Dowler and Madeleine McCann, had suffered “devastating” experiences at the hands of the press. Parts of the industry, meanwhile, had viewed celebrities as little more than “fair game”.

Predictably, Leveson also took aim at the News of the World and Murdoch by commenting:

“Most responsible corporate entities would be appalled that employees were or could be involved in the commission of crime in order to further their business. Not so at the News of the World.”

Only this week, while his report was at the printers, Leveson said he had received new proposals from the industry for a tougher Press Complaints Commission, with contracts to bind members to obey its rulings. Virtually all proprietors were now prepared to sign them, he said. But even this did:

“… not come close to delivering regulation that is itself free and independent of the industry it regulates … Any model with editors on the main board is not independent of the industry.”

Despite the difficulties — technical and political — in finding a solution, his lordship appeared to be remarkably optimistic, despite the history of failure to pull Fleet Street into line.

“No one in their right minds would contemplate an eighth [inquiry],” he said.

His parting shot was that he would take no questions and make no further comment. The report would have to speak for itself. “The politicians must now decide who guards the guardians.”