Love him or hate him (I lean more to the former camp, you may be surprised to know) Tony Blair reminded a lot of people yesterday why he became the most successful political leader of recent times, and the most successful in Labour’s history.

It is not just that he is a good communicator, in a different league to the current PM who is a good PR man (which is different). It is more the fact that he can always analyse a problem, mount an argument, set out both a context and a framework for change.

The stuff on Murdoch, and the interruption by a protestor, inevitably took a lot of the coverage. But in terms of the future, perhaps the most significant point came when he made clear that if Lord Justice Leveson comes forward with radical proposals for change, and David Cameron tries to implement them, he would work to help build all-party support.

When I gave evidence for the second time, Leveson seemed rather troubled when I said I felt cross-party support would be difficult to gain. The reason was that I sensed in a speech by one of today’s witnesses, Michael Gove, who said the inquiry was having a ‘chilling’ effect on the press, the beginnings of a political strategy to get the Tories on the side of the press, and Labour on the side of Leveson.

So much has happened since then however to weaken Cameron, Hunt, Gove and Co, that the dynamics have changed, and empowered Leveson. However close people thought we may have been to sections of the press, it was like a very cold divorce compared with the incessant and incestuous dealings exposed so far. Papa! Yuk.

With witness after witness, Leveson seems to be asking the right questions, and yesterday gave a good idea of the areas where he is applying most of his thinking.

If he comes up with good and workable ideas for a regulator independent of politics and the media, but with real teeth, then Cameron does indeed deserve support in trying to get it through.

One of the disappointing things about this inquiry is that whereas the political class, as TB did again yesterday, have at least acknowledged the need for a change in culture on both sides, the bulk of the press have remained in what Leveson called ‘agressive defensive mode.’ They still don’t get it, and will fight hard against anything they think stops them maintaining the poisonous culture they have created. For papers like the Mail in particular, it is all they know, all that Paul Dacre can do, and they are too set in their ways to change. He is too slow to realise that it is his generation and his style of journalism that is dying out here.

I think I have told here before the story of my conversation with Cameron at Rebekah Brooks’ second wedding, when I said to him that if he became PM, and he decided to do something about the media culture, I would do what I could to get Labour to support him. He seemed to agree something needed to be done, but was unsure what. And of course as the election neared, the political imperative of trying to get the press onside took over, and as the inquiry has already seen, he got sucked in too deep.

The word is that he is devoting every spare moment to preparing for Leveson. Of course he has to have detailed answers to the difficult specific questions he will be asked. But he also needs a strategy – and his strategy should be to indicate that he is confident Leveson is on the right lines, that politics and the media will benefit from media policy being independent of both, that therefore he will almost certainly wish Parliament to implement whatever proposals the judge makes.

It puts a lot of responsibility on Leveson, and would to some extent be a risk for Cameron. But it will get him from where he is – a very bad place – to somewhere slightly better.

He has got to this bad place mainly via the Budget, because it showed that when push comes to shove, he is on the side of the rich and powerful ahead of the many. His stance on the press has confirmed that view, and he needs to shift it. His appearance before Leveson will be a big moment, and big moments are when perceptions can be changed. He should not be thinking whether, but how.