1. Blair denies ever doing a deal with Rupert Murdoch
Asked whether he knew anything of a supposed deal between Murdoch and David Cameron, Blair said he had “no knowledge” of such a deal. He added: "All I can say is Murdoch never made such an approach to me.”
2. Blair says that Murdoch did not lobby him on media policy
The former prime minister said that Murdoch “didn’t lobby me on media stuff” but said that this was “not to say we weren’t aware of the positions their companies had”. These included strong views against European integration. He added that on regulatory matters that had a direct impact on Murdoch’s business, “we decided more often against than in favour”. He added:
Am I saying he's not a powerful figure in the media? Well no, of course he is, and, of course you're aware of what his views are, and that's why I say part of my job was to manage the situation so that you didn't get into a situation where you were shifting policy.
3. He and Murdoch clashed over Europe. . .
This has already been widely reported, but Blair stressed that he and Murdoch disagreed over Europe. He said:
Europe was the major thing that he and I used to row about. I believed in what I was doing, I didn't need him or anyone else to tell me what to do.
As evidence that he had not changed policy for Murdoch, he said:
I would say very strongly we managed the position that I believed in on Europe and that was a position the Sun and the News of the World frequently disagreed with me on.
4. . . But agree on many other things
Blair stressed that on public service reform and trade unions, he and Murdoch happened to agree:
Our views may have coincided. But I believed what I was doing. I did not need him to tell me what to do.
5. Blair sent Rebekah Brooks a supportive message after she resigned
The former prime minister revealed that he sent a sympathetic text message to the former News International chief executive after she was forced to step down last year over phone hacking allegations. He told the inquiry: "I'm somebody who does not believe in being a fairweather friend”. He said that he did not know the facts, but that he felt sorry for Brooks. "I have seen people go through these situations, and I know what it's like”.
6. Murdoch and Blair are closer now than when he was in office
Blair confirmed that he is the godfather of Murdoch’s daughter for the first time (even though the story broke some months ago). He said that while he was in office, he had a “working relationship” with Murdoch, but now it was “completely different”:
I would not have been godfather to one of his children on the basis of my relationship in office. After I left office I got to know him. Now it's different. It's not the same.
He spoke warmly about his friend, saying that the media baron was “not a tribal Tory” who had certain views that were “very anti-establishment”.
7. He does not regret New Labour’s media obsession
Though his government has been demonised and caricatured for it’s obsessive chasing of positive headlines, Blair said that he has no regrets. Stressing the immense power of the press – across the board, not just limited to the Murdochs’ businesses – he said that implementing reform would have derailed his entire policy agenda.
This would have been an absolute, major confrontation, you would have had virtually every part of the media against you in doing it. And I felt the price you would pay for that would actually push out a lot of the things I cared more about. Although I think this is an immensely important question, I don't in the end, not for me, at any rate, as prime minister, was it more important than the health service, or schools or law and order.
8. Anti-war protesters look set to follow Blair wherever he goes
As I reported  earlier, a man interrupted the morning proceedings to shout “this man is a war criminal”.
9.Blair denies ever briefing against colleagues
In what some have interpreted as a veiled comment on Gordon Brown, Blair said twice that he never asked the Sun to attack his enemies:
I did never and would never have asked her or others to conduct attacks on specific individual ... I absolutely hate that type of politics.
He specifically denied claims that No 10 briefed against Mo Mowlam.
10. Blair hates the Daily Mail
While he defended the Murdoch press, Blair had strong words about the Daily Mail:
If you fall out with the controlling element of the Daily Mail, you are then going to be subject to a huge and sustained attack. So, the Daily Mail for me - it attacked me, my family, my children, those people associated with me - day in, day out. Not merely when I was in office. And they do it very well, very effectively. And it's very powerful.
He said that the paper had a “personal vendetta” against his wife Cherie, and that her solicitors sent at least 30 legal warnings to the newspaper between mid-2006 and November 2011.