The media lawyer Mark Lewis, who represents the family of murdered schoolgirl Milly Dowler, said he and the Dowlers are "cautiously optimistic" about Lord Justice Leveson's report.
He said he hoped that the MPs who signed an open letter opposing the statutory underpinning of the press regulator would look again at the proposal.
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More than 80 people are refusing to leave their homes on the Chalcots Estate despite an evacuation of the estate's tower blocks.