The Leveson Inquiry has been a compelling show. After eight months of testimony – from the parents of murder victims, from over-exposed celebrities, from once all-powerful and elusive newspaper proprietors, even from the Prime Minister himself – the panel has trawled through much that was well-known about the operations of the press, and much that was not. With the hearings drawing to a close, the question now is what happens next.

This newspaper's concerns about the inquiry remain. Its remit is too broad, taking in everything from the specifics of phone hacking at News International through to the entire industry's culture, ethics and practices. Within that, whole areas remain, surprisingly and inexplicably, largely untouched, such as the methods and influence of public relations practitioners and the parliamentary lobby. More serious still, it has run in parallel with no fewer than three police investigations – into phone hacking, computer hacking and bribery of public officials – leaving too many questions either impossible to ask or impossible to answer, and prejudice to future trials a real danger.

For all that, there has been much of value. The "network of corrupt officials" described by Deputy Assistant Commissioner Sue Akers would probably have come out anyway, as Operation Elveden progressed. But the Leveson Inquiry has shone a light into the murky world at the top of Britain's power structure that might otherwise have continued unnoticed and unchecked. The culture of chummy text messages and loaned horses, of private dinners and country suppers, revealed by top News International executives and senior politicians, has changed Britain's understanding of itself as a model of rectitude and fair play. And after so much dirty linen so publicly washed, politicians are likely to be more circumspect in future.

Amid the justifiable furore over relations between politicians and the press – not least as regards the Culture Secretary and Rupert Murdoch's BSkyB bid – it has been easy to forget the primary goal. With the evidence sessions over, Lord Justice Leveson now turns to writing his report recommending more effective regulatory arrangements.

The least contentious starting point must surely be that the Press Complaints Commission has failed so egregiously, and is so wholly discredited as a result, that there is no option but to wind it up. The question, then, is how best to replace it. For the PCC's successor to have any credence, all news organisations above a certain size must participate. Unless a way can be found to compel proprietors to take part, the only alternative must be by legal force. The law must be a last resort, given the dangers of statutory regulation, and the threat – real or implicit – to the freedom of the press, but it cannot be ruled out. With that, the state's role must be over: the rules to be observed, and those charged with policing them, must remain wholly independent.

To be successful, the new watchdog must also have disciplinary powers. With both its remit and its personnel clearly separate from the government, the proposal of licences or cards for journalists – which may be withdrawn if the rules are broken – makes sense. A strong code of conduct, a swift and robust complaints procedure and the capability to levy significant fines would also work well, without the risk of encroaching on the vigour and independence of the press.

Such issues are no small matter. Britain is rightly regarded as a beacon of free and effective journalism. Likewise it must be said that, for all the appalling misconduct of the phone-hacking scandal, the vast majority of journalists behave with integrity and rectitude. While there is a clear need for more potent oversight, Lord Justice Leveson must not allow the valuable contributions of the many to be sacrificed to the transgressions of the few.