A further 15 pending cases could be halted if they are found to rely too heavily on professional witness statements when there was no sign of physical violence.
Lord Goldsmith, the Attorney General, announced the wholesale review, which turns child abuse orthodoxy on its head, after a "serious and far-reaching" judgment by the Court of Appeal in the case of Angela Cannings, 40.
On the basis of expert evidence, she was wrongly convicted, of killing her babies, seven-week-old Jason, and Matthew, three months.
Lord Justice Judge, sitting with Mrs Justice Rafferty and Mr Justice Pitchers, ruled that in future no parent who had lost two or more babies should be prosecuted if the case relied solely on expert evidence that was disputed by other professionals who believed that the death could have been caused by natural, if unexplained, causes.
He acknowledged that some women who did kill their babies could escape justice as a consequence, but that "undesirable result" was better than innocent women being jailed for life.
The changes were necessary given the number of cases of women wrongly accused of killing their babies which had come before the courts last year, he said.
Lord Goldsmith said shortly after the ruling: "I share the unease expressed by the Court of Appeal."
He said that 258 convictions of parents over 10 years for infanticide, murder and manslaughter were to be reviewed "as a matter of urgency". Of those, 54, in which the parents were still in jail, were to be given the highest priority.
Lord Goldsmith said: "These cases will be considered further as a matter of urgency to establish whether they bear the marks of a conviction which the Court of Appeal judgment has indicated may be unsafe."
He hoped the review would be completed within weeks.
Any cases which fell within the court's criteria as unsafe would be passed to the Criminal Cases Review Commission to consider an appeal.
The Crown Office in Edinburgh said it would also be examining the ruling but said there were differences in how evidence was corroborated between courts in Scotland and England.
Lord Justice Judge's ruling follows the quashing of 39-year-old Sally Clark's conviction in January last year for killing her two babies and the acquittal of Trupti Patel, 35, for killing her three babies.
In each case the Crown called Prof Sir Roy Meadow, a consultant paediatrician who promotes the proposition that one baby death is a tragedy, two are suspicious and three are murder unless proved otherwise.
Lord Justice Judge said that Mrs Cannings's conviction was unsafe on the grounds of "significant and persuasive fresh evidence" which "demonstrably undermined" the Crown's case.
She had "cherished" her babies and was faced with recurring disasters, losing her two sons after the death in 1989 of her first child, Gemma, whose death was not the subject of a charge.
Lord Justice Judge said new research showed that there was now "acceptable evidence that even three infant deaths in the same family might occur naturally and all properly be described as sudden infant death syndrome".
He said: "In our judgment the mere fact that specific natural causes were not established for any of the deaths did not lead to the inference that the infants were smothered or deliberately harmed, but rather left open the possibility that sudden infant death syndrome should not be excluded."
Lord Justice Judge said that further research was needed. But for the moment, "in cases like the present, if the outcome of the trial depends exclusively or almost exclusively on a serious disagreement between distinguished and reputable experts, it will often be unwise, and therefore unsafe, to proceed".
Mrs Cannings, who spent 17 months in prison, and her husband, Terry, of Salisbury, Wilts, refused to comment as they left court.
William Bache, their solicitor, said the judgment was "a tour de force" and "a monument to justice and common sense".
John Batt, a solicitor who was part of the Sally Clark defence team, said: "Finally the penny has dropped. These are desperate and grieving mothers who are being treated like some kind of Myra Hindley."
Mrs Clark's father, Frank Lockyer, said the comments made by Lord Justice Judge were a "huge step forward".
Mr Lockyer, 73, speaking on behalf of his daughter, said: "For a long time now we have been saying that the criminal court is not the place to find out how a baby has died."
Sir Roy, who is facing an inquiry by the General Medical Council into allegations of serious professional misconduct, was not available for comment.
Ministers are reviewing an estimated 5,000 child protection order cases in which he was involved over the past 15 years in the family courts.
Margaret Hodge, the children's minister, has ruled out returning the children to their families but said that any parents who felt they had been wronged could go back to the family court.
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