Murdoch-owned News International has “too much” control of Britain’s newspaper market, Ed Miliband has told the Leveson Inquiry.The Labour leader said today the “arrogance” of Rupert Murdoch’s company came from its 34 percent market share. He asked Lord Justice Leveson to consider a limit on cross-media ownership and said it had been included in the inquiry’s terms of reference during discussions with David Cameron and Nick Clegg.He said: “I don't believe that one person should continue to control 37 percent, or it's now 34 percent post the Sun on Sunday, 34 percent of the newspaper market.“My strong instinct is that's too much and, I would like to see the inquiry looking at the question of whether we should have lower limits. There's a question of about where these limits should be set. I should say we should have no worries of someone owning up to 20 percent of the newspaper market. I think there is then a question of between 20 percent to 30 percent where you should set a limit.“That's where I'm coming from. I think it's good for our democracy to have plurality in the market.”Miliband said there was a huge responsibility on politicians to make sure the inquiry’s recommendations for press reform were enacted and promised the judge he would seek to work with other ministers on a cross-party basis.The opposition leader admitted he had been too slow to act on allegations of phone hacking at the News of the World, calling it a “failure of the establishment”.He added: “The failure to get to grips with this earlier was a failure on the part of the police who failed to adequately investigate it, and politicians who, with a few exceptions, failed to challenge early enough what was happening.”Miliband first called for a public inquiry into the scandal on July 5, and told the inquiry he knew he was “crossing a Rubicon” because it would be seen by News International as an act of war. He also called for chief executive Rebekah Brooks to consider her position.Earlier that year, Tom Baldwin – the party’s director of communications – had written to Labour MPs dissuading them from linking News Corporation’s bid for BSkyB with phone hacking.Miliband said he should have raised phone hacking with Rupert Murdoch at the June 2011 News International summer party. Records showed the he had 15 contacts with the company from September 2010 – when appointed leader of the opposition – until July 2011 but only one since the hacking scandal broke.He said he spoke to James Murdoch on March 3, 2011 about the BSkyB bid but described it a courtesy call. He took a phone call with Brooks in December 2010 following the removal of business secretary Vince Cable from overseeing the bid.Robert Jay QC, inquiry counsel, asked whether Miliband was aware Ed Balls, Charlie Whelan or Damian McBride had briefed against Tony Blair when prime minister.Miliband said he had raised concerns with Brown about McBride’s activities in 2009 and Whelan was well-known for briefing, but had no knowledge on Balls.