However Nick Johnson KC, who prosecuted the original trial, said in written submissions that the defence application was “misguided” and the jury had found Letby to be a “multiple killer and habitual liar”.
Lord Justice William Davis, sitting with Lord Justice Jeremy Baker and Mrs Justice McGowan, said at the start of their ruling they would “refuse permission” for Letby to challenge the conviction.
In a ruling briefly interrupted by a fire alarm inside the Royal Courts of Justice, he said the Court of Appeal had to take into account the “unrivalled” experience of the judge in charge of both trials and the steps he took to ensure the second prosecution was fair.
Lord Justice Davis said: “We conclude that the judge was right to find that Letby would be able to have a fair trial.”
He added the suggestion police should not have spoken about the case was “fanciful”.
Letby, who watched the hearing via a video link from HMP Bronzefield, showed no reaction as the judges gave their ruling.
She had previously been sentenced to 14 whole life orders for the murders of seven babies and the attempted murders of six others, with two attempts on one child, and was sentenced to a 15th whole life term for the attack on Child K.