So, finally the bogeyman has arrived. A regulated press! Government intervention! Stalinism! Precious liberties won through 300 years of courage and eloquence to be forfeited by a panic about phone hacking! Ever since Lord Justice Leveson began his inquiry into what he charmingly calls the "culture, practice and ethics of the press", the public's flesh has been made to creep in this manner about an attempt to ensure that the press behaves in a remotely civilised manner.

Leveson's clever report does call for a new system of regulation backed by the force of law, but most of us who have been involved in investigative journalism in the public interest for many years will find it hard to fault what he says, either about the imperative of reform or the futility of once again accepting on trust promises from the worst of the press, its editors and its owners. The serial misconduct, as Leveson makes clear, has been confined to a relatively small number of miscreants with News International in the lead (and but for the Guardian, the misdeeds would have gone unpunished).

But Leveson's indictment of the reckless crimes of phone hacking, computer intrusion, harassment, spying and bullying is chilling to read, just as it was terrifying to experience for the victims, the humble and celebrated alike. The intrusions into people's lives without any real public interest justification have a long, sordid history and are too numerous for the recidivists to be given just one last chance, guvnor.

There are many weaknesses in the report, on which more in a moment. However, on the central issue – which the prime minister disputed on Thursday – I believe Leveson deserves support. He is right to argue that the new system of self-regulation must be underpinned by statute. This would give credibility to the self-regulators, who would be wholly independent of any government or government department.

Leveson believes such statutory underpinning is "essential". It would enshrine for the first time a legal duty of the government to protect the freedom of the press. It would reassure a public whose faith in the press has been sadly diminished. It would give the ring of authority to the standards promulgated by the successor to the Press Complaints Commission – what we could call a "Press Trust" – and its proposed system of arbitration in disputes. I do have my doubts, however, about whether Ofcom is the right body to watch over all this.

His description of a new system whereby the press would regulate itself is convincing in its detail. He has introduced incentives to encourage all publishers and editors to co-operate, whether in print or on the internet. I like the five ways he strives to create a credible system based on the establishment of a Press Trust. It sounds similar to the BBC Trust (which remains a good model, despite recent accidents at the BBC).

This trust would monitor a genuinely independent and effective self-regulatory system dedicated to promoting high standards and protecting the rights of individuals. It is important, as Leveson recognises, that most of its members should be independent of the press – though it should include a number of people of experience such as a former editor and investigative journalist, and certainly should not include any member of the government or Commons. This should appease the paranoid, but don't count on it.

The new trust would require the industry to provide adequate funding. Since print is in difficulties, I suggest the pockets be tapped of those who make oodles on the net, including Google. A more difficult question is how this body would adjudicate complaints and initiate its own inquiries with equal care for the sensitivities of individuals and complexities of investigative journalism.

The press – who dat? – would have to agree some form of selection process for the trust. The trust, in turn, would be served by a new "code committee" on which experienced press people would have an important role. I believe it should act with the utmost openness.

Leveson is very shrewd in building incentives for all publishers to support the new system, with increased civil penalties for gross intrusions of privacy by those who have decided to stand aside from the arbitration services the trust would provide. New civil procedure rules would permit the court to deprive the recalcitrant publisher of a claim for damages in suits about privacy, defamation and similar media cases even when he had succeeded at trial.

The biggest disappointment in Leveson is how far he skates over the crucial issue of ownership. It matters very much that the law on competition was broken by Margaret Thatcher's participation in 1981 in a secret deal by which Times Newspapers came under News International's control. All Leveson's fine language in his report about the need for future transparency is justified by the vaguest of references to what made it necessary in the first place. It surely matters a great deal that the greatest concentration of the British press was achieved by a backroom deal that gave News International such sway over British public life.

The voluminous report is also unwilling to reconcile all the conflicting testimonies of various witnesses. Was I telling the truth about Thatcher and her deal to give Rupert Murdoch control of Times Newspapers or was I not? Was Gordon Brown telling the truth about the pitiable exploitation of his newborn child, or was Rebekah Brooks?

Leveson, though, is highly critical of Murdoch's attention to what was going on in the News of the World. In his report he writes: "Although Mr Murdoch would no doubt not wish to countenance the deployment of tactics tantamount to blackmail, his more general observations about the doing of favours and back-scratching are extremely revealing as to the culture, practices and ethics of the press more generally, and far more so than simply in the circumstances which he was then discussing."

In the Commons exchange between the prime minister and Labour leader there was both dissent and agreement. The dissent was Ed Miliband's acceptance of the idea of statutory underpinning for the new Press Trust. Perhaps the prime minister was being shrewd in withholding his own endorsement of this idea. His emphasis was, like Miliband's, on the press now moving with all deliberate speed on Leveson's recommendations for setting up the new system of self-regulation. There was an implicit warning here that if they didn't, there was always the possibility that Cameron, Clegg and Miliband would all unite on the disputed issue. The prospect of a hanging, as Dr Johnson said, concentrates the mind wonderfully.