Reporting restrictions on the case forbid naming the mother and her partner, who have been convicted along with their lodger Jason Owen for causing the death of the 17-month old baby, known as P.
"It would be in no one's interest and certainly not in the interests of justice for the public to get the impression that the press is covering up," he said.
The evidence of text message campaigns and social network sites showed that members of the public believed the press were conspiring to keep the names secret, he said.
Anyone with internet access can read all of the things which the press is not allowed to report and which would be in contempt to report, added Satchwell.
Combined with his other arguments for reform, as reported by Journalism.co.uk in September, Satchwell said this recent case 'added weight' to moving the debate forward.
The answer is not to police the internet, he said, adding that this would be an 'impossible' task.
While emphasising that he does not want to go down an entirely Americanised route with televised trials and post-trial juror interviews, Satchwell said the UK system should take its lead from the American 'good faith in the jury' method.
"What the Americans say is that you've got a jury system so you have got to trust the jurors and assume that they probably will go and look on websites," he explained.
It is ironic that the reason reporting restrictions are in place is to make trials fair, but in cases like Baby P's these have had the opposite effect, he added.
"What is happening inadvertently, because of the internet, is that some people are suggesting that the media is conniving with the courts to suppress information which they feel they are entitled to know.
"That in itself is not helpful to the administration of justice [...] because people's confidence is based, among other things, [on the fact that] the media provides fair and accurate reports," Satchwell said.
Satchwell's plea has been heard by the Attorney-General, he said, adding that debates between journalists, lawyers and judges were already happening with the general tendency 'even amongst senior judges, towards some kind of liberalisation'.
"This is not not likely to happen urgently or quickly overnight. There is a debate going on and there are many facets to that debate," he said.
Related Journalism.co.uk links:
Blog comment: Naming Baby P is not about giving into a Facebook campaign
Restricted Reporting: 'What's the future for contempt of court?' Bob Satchwell interviewed.
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