James Murdoch has a great deal of explaining to do.

The former head of News International told the Commons media committee this week that the first inkling he had that phone hacking at the News of the World went further than a single rogue reporter was in December 2010. Mr Murdoch claims that when he authorised out-of-court payments to a high-profile hacking victim in 2008, he was kept in the dark by subordinates about the full scale of the illegality that had been taking place at the newspaper.

But this week, two of those executives took issue with that narrative. On Thursday, the former News of the World editor, Colin Myler, and the newspaper's legal manager, Tom Crone, released a statement saying that in 2008 they drew Mr Murdoch's attention to an email that blew a large hole in News International's claims about hacking being the work of one rogue reporter.

So who is telling the truth? Colin Myler and Tom Crone? Or James Murdoch? If it turns out to be Mr Murdoch who is dissembling, then he is in serious trouble. For that would imply that he has lied to the public, misled Parliament, knowingly covered up gross illegality at News International and perhaps even obstructed the course of justice.

It will have wider implications too. The News Corp chairman and chief executive, Rupert Murdoch, told the Commons media committee this week that his company takes a zero tolerance approach to wrongdoing. Yet the possibility now arises that the former head of News Corp's British subsidiary was prepared to sweep serious wrongdoing under the carpet. And, of course, James Murdoch has since been promoted to a senior position in News Corp (and is often spoken of as the successor to his father as head of the company). If this is what has happened, can News Corp, under its present management, seriously be considered "fit and proper" to own media organisations in the UK?

Two things must now happen. The committee's chairman, John Whittingdale, says Mr Murdoch has agreed to write to him to explain his testimony further. But this discrepancy demands more than an exchange of letters. Mr Murdoch, along with Mr Crone and Mr Myler, must be called to testify again before the committee to get to the truth. This should happen within weeks, despite the fact that the summer recess has begun.

Mr Murdoch also needs to be questioned by the police about his testimony. The focus of the Metropolitan Police's Operation Weeting has apparently been on the narrow issue of phone hacking. And that is a big enough job. According to Deputy Assistant Commissioner Sue Akers, who is leading the investigation, only 170 out of some 4,000 phone-hacking targets have so far been contacted. Yet as well as pushing on with that, the police must not neglect to probe this suspected cover-up.

From the start, the phone-hacking affair has been as much a scandal of the apparent immunity of the Murdoch empire as it has been about illegal eavesdropping. For a long time it looked as if one newspaper group was, in effect, above the law thanks to its connections at the very top of politics and policing. That any institution or individual should be in such a position is incompatible with democracy. This is why it is now so vital that the police investigate with the utmost seriousness the possibility that James Murdoch has broken the law.