The terms of reference of the Leveson inquiry set out the widest review of the media since the Annan Report in the 1970s. But are they too broad? Will they – by broadening the debate beyond News International to include press, social media, broadcasters and even the BBC – deflect attention from the most severe failures at News International?

Much will depend on the leadership of the inquiry and the extent to which Lord Leveson and his panel can set the agenda. The Media Standards Trust – rather than some sinister News International conspiracy – lobbied for the broadening of the inquiry to include other media, and the relationships between politicians and the media. These "Part 1" issues are separated in the inquiry terms of reference from the "Part 2" issues which focus on the specifics of News International, but of necessity are not limited to that one group. If the inquiry is to be successful, Leveson would do well to maintain a clear separation between these parts in terms of report, timing and process.

Any long-term solution to the problem must take on the broader issues. Each of the three main party leaders, in one way or another, has accepted a clear narrative which explains what got us into this mess. They have accepted that there is one thing that links all the questions addressed by the inquiry: why did the phone hacking take place? Why did a series of police investigations fail to root it out? Why did politicians fail to act on the ICO report from 2006? The unspoken hypothesis that links all of those questions is media power: was this media power run amok? Fundamentally can all the buck-passing, policy compromise and political heads wanting to remain firmly below the parapet as regards anything to do with the press be explained by one root cause: that the political price to be paid for addressing any of those issues in a way that impacted "our friends in the media" was too great? News International – because of its size and cross-media scope – is the clearest example of this but not the only one.

David Cameron has clearly accepted the core of this narrative, because he has already in the debates on Wednesday called for a new system of media pluralism monitoring as a response to the crisis. In doing so he clearly accepts that a proper policy response must reflect the wider question of media power, as well as the specifics of the crimes that have taken place.

The prime minister's attempt on Tuesday to draw a comparison between alleged BBC bias and News International is shocking in the current circumstances, but after a moment's reflection is not likely to convince the committee or anyone else to shine a spotlight on the BBC. The difference between the two organisations' governance and accountability structures, particularly as regards newspapers, couldn't be greater. And it is precisely the failure of accountability and governance – caused by media power – that is at stake here.

The public does have to be vigilant as this process unfolds: there is a danger that the inquiries will be subject to the old pressures and negotiations between the press in particular and pliant politicians. Media policy has always been a hotbed of intrigue and back-scratching between them. The difficulty for the inquiry will be to ensure that it is above all that. All evidence must be transparent, all sessions open. And the panel members must be prepared to be deeply unpopular.

But in one respect the terms of the inquiry may yet prove too restrictive. Might they set out some distinctions between different media that are becoming outmoded? The inquiry team are asked to produce recommendations to support "the integrity and freedom of the press, the plurality of the media, and its independence, including from government, while encouraging the highest ethical and professional standards." The press, here, are to be free, while the media – presumably broadcasters – are merely independent. While this reflects the old regime there are good reasons to wonder whether this approach should be questioned. Too often, press freedom is a shorthand for anarchic self-regulation rather than subtle balancing that accepts necessary and agreed limits to press freedom, such as the freedom to invade privacy. If "press freedom" is shorthand for a veto on parliament setting out the standards that a self-regulatory body should impose on the press then the term should be jettisoned. If it cannot be jettisoned, Leveson should grab the initiative by offering his own definition.

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