Mayor of London Boris Johnson told ITV News, during a visit to India, that he did not "think it would be right to come up with statutory legislation" ahead of the publication of Lord Justice Leveson's report into press standards.
He added: "You need to have a free press to have a free society. If you want to keep the gutters of public life clean you need a gutter press."
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Nabi Tajima, who was the last known person to have been born in the 19th century, died in Japan after being in hospital since January.
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Hunt accused companies of "turning a blind eye" to a generation of children "exposed to harmful emotional side effects" of social media.