The Hacked Off campaign, which represents many victims of newspaper intrusion, said Lord Justice Leveson had given the Prime Minister a "workable, proportionate, reasonable solution" to the problems of press abuse.
But the group added that David Cameron "had not done his job" by failing to accept the full recommendations of the report and was wrong to trust Editors to "behave themselves".
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A further 85 buses are expected to arrive on Tuesday and Wednesday, with officials saying the entire operation will last at least a week.
The reality star had filed a defamation lawsuit against celebrity gossip site MediaTakeOut.com.
The model and reality TV star said she had "never been so scared in my life" after finding Shavaughn McKenzie lurking in her driveway.