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
Tributes pour in for Wolves legend and cricket trailblazer Baroness Rachael Heyhoe Flint.
The flags at Molineux are flying at half mast to mark the passing of Wolves Vice-President Rachael Heyhoe Flint.
A child rapist from Nottingham who was caught after his 10-year-old victim took part in a school assembly has been jailed for 15 years.