Bob Satchwell, executive director of the Society of Editors, says the McCanns are wrong to think that the tough new self regulatory regime requires a statute.
No-one – including politicians of all parties, really wants to see that with the inherent long terms dangers, so long as another form of guarantee about the independence of the system is put in place.
"The Leveson principles are not being undermined and the provisions of the strict new system, with fines of up to £1m, demonstrate that the press has not been let off any hooks."
He added that Lord Justice Leveson recognised that the "vast majority" of journalists were "blameless", adding: "There are complex practical and legal issues in implementing the new system, but the Leveson pathway will be closely followed.
The McCanns say they don't think new plans to regulate the press suggested by the Leveson Inquiry are tough enough.
More top news
A village pub in Nottinghamshire hopes interest in an air crash 50 years ago will help provide the local air ambulance with a new helipad
A Nottingham man who admitted raping and sexually assaulting a young girl has been jailed for 17 years.
Low levels for the Bank Holiday weekend