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."
– Bob Satchwell, Society of Editors
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.
Kate McCann: the proposals are a 'compromise of a compromise'
While giving evidence at the Leveson inquiry into press standards last year, Kate McCann said she felt like "climbing into a hole and not coming out", after the News of the World printed her personal diary which she started writing after her daughter disappeared.
Speaking on the Andrew Marr show in BBC Ones this morning, Mrs McCann said:
"What the Government is proposing with this Charter - the charter body is overseen by ministers for a start which again takes away the independence - it is basically a compromise of a compromise.
"Why do the press, the Government, not want to be accountable like everybody else? The press are the first to hold people in authority to account."
– Kate McCann, speaking on the Andrew Marr show in BBC One
McCann's criticise proposed changes to press regulation
Kate & Gerry McCann, whose daughter Madeleine went missing from a holiday apartment in Portugal in 2007, have criticised proposed reforms in the regulation of the press in the wake of the Leveson Inquiry.
The coverage in the newspapers of the four-year-old's disappearance was given by Lord Justice Leveson's inquiry into press standards as an example of how stories ran "totally out of control".
Speaking on the Andrew Marr show on BBC One this morning, Mr and Mrs McCann said plans for a new press regulator backed by a Royal Charter do not do enough to hold the press to account, describing it as "a compromise of a compromise".
More than sixty thousand people have now signed an online petition calling for the Leveson recommendations on press regulation to be implemented in full.
The petition was launched yesterday by the father of Madeleine McCann from Leicestershire. The Prime Minister says he's opposed to a press watchdog backed by law. Victims of phone hacking victims, including 7/7 hero Paul Dadge from Staffordshire, say they feel they have been let down.
Gerry McCann: "The public support is overwhelming"
by Alison MacKenzie
Gerry McCann speaking outside the Houses of Parliament today. He said the public's support following the Leveson report have been overwhelming. He added "politicians should listen to the public, if they don't, they usually run into problems."
The father of missing Madeleine McCann said legal backing for any new system was the "minimum acceptable compromise for me and for many other victims" and urged the Prime Minister to "do the right thing".
He told the BBC Radio 4 Today programme: "I would have liked to have seen a properly independent regulation of the press, whereas I think he has given the press another opportunity of self-regulation."
It should be made compulsory and measures put in place make journalists more accountable, he said.
He added: "But I do accept that full implementation of Lord (Justice) Leveson's report is the minimum acceptable compromise for me and I think for many other victims who have suffered at the hands of the press.
"The Prime Minister and our other elected politicians have an opportunity now to do the right thing. And if they do the right thing, for the public, then it will help restore a little confidence.
"I clearly respect his opinion but I personally disagree with the viewpoint and Lord (Justice) Leveson, as a senior law judge of our country, has made clear that what he is proposing is not a state-run press.
"It is a fine distinction but without the statutory underpinning this system will not work."