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Police already have arrested eight people in connection with the hacking scandal, including Andy Coulson, Mr. Cameron’s former communications director and former editor at the News of the World.

“There is a firestorm that is engulfing parts of the media, parts of the police and indeed our political system’s ability to respond,” Mr. Cameron said.

Jason Walsh reported in Dublin, Naomi Westland reported in London, and Jabeen Bhatti contributed to this report from Berlin.