Labour minister Jack Straw has claimed Rupert Murdoch "seems to enjoy playing with political leaders".The MP, who held several senior positions under the Labour government, said the proprietor is interested in power and using political connections to help open doors on media policy.During his evidence to the Leveson Inquiry today, Straw admitted he had “no more than a paragraph-worth of conversation" with the News Corporation founder, but formed the view Murdoch was “interested in power for its own sake”. Asked whether support was ever offered to Labour, Straw said Murdoch would back the winning party “in return for what he thought he could get out of it”.He added: “I don’t mean a deal, because I’ve seen no evidence of a deal.”Straw said he was aware Tony Blair had three phone conversations with Murdoch leading up to the Iraq war in 2003 but denied they had any influence over cabinet discussions, which he said would be “disgusting were it true”.He added: “When Mr Blair came into power we all took the view that it was best to get the papers on our side, without compromising ourselves.”He admitted the Blair government was too close to some journalists from being in opposition, and carried the relationship on after the 1997 election. He claimed opposition spokespeople often built up “very, very close, sometimes incestuous” relationships with political correspondents. He later told the inquiry he was "furious" after discovering a leak of the Lawrence report from Number 10, and had launched internal enquires. The individual responsible did not face action but later left Downing Street.Robert Jay QC, inquiry counsel, asked Straw about his contact with Rebekah Brooks, after his witness statement revealed the pair “made arrangements” to sit together on a train from Oxfordshire to London.He told the inquiry: “We would talk about what was in the papers. We'd gossip about personalities, and that sort of thing. We weren't nattering the whole journey.”The journeys stopped in 2009 when Brooks was made chief executive of News International and changed her travel arrangements. Straw later said Brooks had “persistently lobbied” him over the News of the World’s 'Sarah’s Law' campaign in 2000. Last week the former executive told the inquiry the campaign was launched on behalf of the paper’s readers.In reference to the recent resignation of Jeremy Hunt’s special advisor, Adam Smith, over contact with News Corporation, Straw claimed he would have been aware if his own had “acted inappropriately”.He told the inquiry: “I knew what they were doing and I knew in real time what they were doing.“If there had been a moment where they had acted inappropriately then somebody else in this very open environment, I mean ring of informality but very open environment itself, would have told me. The Private Secretary, the Permanent Secretary, a press officer - they just would have found out immediately."On privacy, Straw said Parliament should “take this job on now” and introduce legislation instead of relying on judge’s decisions in court under the Human Rights Act, to show people "that they do have the right to have their privacy protected". He said the press were “desperate” to uncover the new identities of Robert Thompson and Jon Venables, after they were released from prison, for the murder of Jamie Bulger, in 2001.He added: “If the identities of these people had been disclosed, they would have been at very serious risk of physical danger, injury, certainly, worse possible and yet some of the papers simply weren’t willing to think about that... I stuck to my guns on that.”The former Justice Minster said he regretted the penalty for breaching the Data Protection Act was “too low” and told the inquiry how Brooks, Daily Mail editor Paul Dacre and Telegraph Media Group executive Murdoch MacLennan had lobbied him over the introduction of jail terms for breaches.He said he dropped that part of the Data Protection Bill to pass it quickly as other policy areas, including prisons, were affected, but said the amendment to section 55 of the Act – concerning the obtaining and selling of data – should now have been introduced.Asked about conditional fee agreements, which he also discussed with Brooks and Dacre, Straw said he was faced by contrasting evidence from local and national press, and law firms. Lord Justice Leveson pointed out most people were unable to afford libel and privacy actions against the press before CFAs to which Straw said he had seen them being misused, leaving small local papers with large legal bills.Straw accused journalists of being “quixotic” and lacked the understanding of what it feels like to make decisions, adding “there is a degree of voyeurism about the British press”.He advocated press regulation with a statutory backing – saying self-regulation allowed editors to be “judge and jury in their own courts” – but admitted there will be a "concerted effort" by some newspapers to oppose plans.He assured Leveson: “There will be that continuing momentum for change and some of us are going to do our best to ensure that it takes place.”