John Tulloch, whose phone was hacked after he survived the 7/7 London bombings, has told Daybreak that there are "a large number of people calling for the regulation of the press."
He said: "Lord Leveson, a large amount of the public, the leaders of two parties and a large number of victims of the media [are calling for it]. That's quite a big argument."
A man who won libel damages after his arrest over the murder of a woman has written to MPs asking them to back Leveson's recommendations.
About 2,000 editors will sign up to a new independent press watchdog, the chairman of the Press Complaints Commission has said.
The Prime Minister has taken a political gamble by holding differing views to the victims, the Leveson inquiry and a majority of MPs.