A solicitor serving life for murdering her two baby sons lost her appeal against conviction yesterday.

The Court of Appeal in London rejected fresh expert evidence said to support Sally Clark's claim that her babies were victims of cot death, or at least ''unascertained death''.

Lord Justice Henry, Mrs Justice Bracewell, and Mr Justice Richards said the case against Clark was ''overwhelming''.

Clark, a 35-year-old corporate lawyer who was given two life sentences at Chester Crown Court last November, has always denied killing 11-week-old Christopher, and Harry, aged eight weeks, at the luxury home she shared with her lawyer husband Stephen in South Oak Lane, Wilmslow, Cheshire.

She insisted that Christopher, who died in December 1996, and Harry, who died in January 1998, were victims of Sudden Infant Death Syndrome (SIDS), known as cot death.

Clark, a policeman's daughter, originally from Devizes, Wiltshire, told the jury during her three-week trial that she had found both boys ''limp and lifeless'' and was in ''complete disbelief'' at having lost two children.

Sitting in the Court of Appeal dock, Clark burst into tears as yesterday's decision was announced.

At an appeal hearing earlier this year, the judges heard new evidence challenging some of the findings made by pathologist Dr Alan Williams, who carried out post mortem examinations on the children.

And two statisticians were called in relation to the prosecution's assertion that the odds of two cot deaths in the same family were 73 million to one.

Clark's lawyers argued that the jury might well have translated this statistic as meaning the chances of innocence were 73 million to one against. The appeal judges said the fresh medical evidence ''does not have any possible effect on the safety of the convictions''.

In fact, had the evidence been heard by the jury, it might even have undermined the defence case, as it was capable of affirming the credibility of Dr Williams.

The judges agreed that the prosecution adopted an erroneous approach to the statistical evidence, and that approach appeared to have been endorsed by the trial judge, Mr Justice Harrison, in his directions to the jury.

But in the context of the trial as a whole, the point on statistics was of minimal significance and there was no possibility of the jury having been misled.