London (CNN) -- Former British Prime Minister Tony Blair came under "political pressure" from media baron Rupert Murdoch during his time in office, he testified Monday at an independent inquiry set up in response to phone hacking and alleged police bribery at Murdoch newspapers in Britain.
Asked if he was "too cozy" with Murdoch, as current Prime Minister David Cameron says many in the British political establishment have been, Blair denied it.
"Coziness is not quite the way I would put it. You were in a position where you were dealing with very powerful people," he said, elaborating on the power of the British press, a theme he referred to frequently. "If they were against you, they were all-out against you."
Separately, London police announced the arrest of a 42-year-old woman in connection with their probe into phone hacking.
The woman was arrested Monday morning on suspicion of money laundering, police said without naming the woman.
The arrest came as Blair was testifying at the Leveson Inquiry into British press ethics.
He said the relationship between the press and politicians is complicated.
"The relationship is one in which you feel this pretty intense power," he said.
UK panel: Murdoch 'turned blind eye' But he said his government had not acted on behalf of Murdoch's business interests.
"Actually we decided more stuff against the Murdoch interest than in favor of it," Blair said. "Pressure from him was more political than commercial."
"He didn't lobby me on media stuff," Blair said, adding: "That's not to say that we didn't know what his position was. But the bulk of our conversations were about politics."
He confirmed that he is the godfather of one of Murdoch's children, but said that is because his relationship with the media magnate changed once he was no longer prime minister.
"I would never have become godfather to one of his children on the basis of my relationship with him while I was in office," he said, but their relations became "easier" after he stepped down in 2007.
He briefly addressed his trip to meet Murdoch on Hayman Island in 1995, while he was campaigning to become prime minister, and agreed with his former aide Alastair Campbell that he was "angered" to have to do it.
Murdoch's best-selling Sun tabloid famously switched allegiance from the Conservative party to Blair's Labour party before the 1997 election that swept Blair into power. But Murdoch insisted strongly that there had been no quid pro quo with Blair for the support of his papers in 1997.
"I, in 10 years in his power there, never asked Tony Blair for any favors and never received any," Murdoch said in April, pounding his hand on the table for emphasis.
On Monday, Blair said he believed Murdoch himself made the decisions about who his British newspapers supported, not underlings.
He said that as party leader, he had paid a great deal of attention to how the Labour party got its message out, portraying it as a necessary part of contemporary politics.
And he said he had decided not to take on the power of the press.
"I took a strategic decision to manage these people, not confront them. You would have been in a huge battle with no guarantee of winning," he said.
Blair's testimony was briefly interrupted by a protester shouting: "This man is a war criminal!"
The man identified himself to CNN as David Lawley-Wakelin, who made a documentary film called "The Alternative Iraq Inquiry."
He accused Blair of taking money from the bank JP Morgan for the invasion of Iraq, a charge Blair made a point of denying once the protester was removed. It took three security officers to pull him out of the courtroom.
The protester appeared directly behind Brian Leveson, prompting the shaken-looking judge to say there would be an immediate inquiry into how the man got into a secure area. The protester appeared to be wearing some kind of pass.
The Leveson Inquiry was established after British public anger at Murdoch's News of the World about the hacking of voice messages of a missing teenage girl who turned out to have been murdered.
The case of Milly Dowler came on top of apologies from the tabloid for the hacking of the phones of celebrities and politicians, and proved to be the last straw for the paper, which was shut down in July.
Cameron set up the Leveson Inquiry to explore press ethics in Britain more widely, alongside police investigations into phone hacking, e-mail hacking and police bribery by people working for Murdoch's British newspapers.
More than 50 people have been arrested. Prosecutors this month announced charges against six people, including Rebekah Brooks, a former News of the World and Sun editor who later became chief executive of News International, the British newspaper publishing arm of Murdoch's News Corp.
She, her husband and four others are charged with interfering with the police investigation.
Blair's former director of communications said this month that the relationship between the press and the political elite in Britain was too cozy.
"I've been arguing for some years (that the relationship) got itself into a very, very bad place, and I hope it can lead to change," Alastair Campbell told CNNI's Christiane Amanpour.
"It's not just about Rupert Murdoch," he said. "We have a lot of newspapers in a geographically fairly small country. ... And I think any political leader has to take account of the role they play in the political debate."
Campbell, a former newspaper editor who became Blair's spokesman when the Labour party was in opposition in the 1990s, said he hoped "some form of proper regulation" would arise from the hacking and bribery scandal.