The Court of Appeal, in London, upheld a jury's verdict in July 1998 that Jenkins, 41, battered the girl to death with a metal tent spike in the garden of the family home in Hastings, East Sussex. After the judgment, Anthony Scrivener QC, representing Jenkins, applied for leave to appeal to the House of Lords. His application will be heard in the Court of Appeal in January.
Thirteen-year-old Billie-Jo was painting the patio doors at the rear of the family's home when she was murdered on 15 February 1997. Tiny droplets of blood found on Jenkins's clothing were the crucial evidence in the trial.
The prosecution told Mr Justice Gage and the jury at Lewes Crown Court that the 150 microscopic blood spots, which were identical to Billie-Jo's blood, could only have got on to Jenkins's shoes, trousers and jacket when he attacked her. The prosecution said the girl would not have been alive 15 minutes later, when her foster father said he found her, and that a dying person's breath would not have produced that kind of spotting.
Five grounds of appeal were rejected yesterday, including fresh evidence from David Denison, a physiologist at the Royal Brompton Hospital in London. Professor Denison had done experiments to show that the specks of blood could have landed on Jenkins's clothing as Billie-Jo exhaled air mixed with blood through her nose when he tended to her as she lay dying.
The three judges at the Court of Appeal, Lord Justice Kennedy, Mr Justice Dyson and Mr Justice Penry-Davey, concluded that Professor Denison's theory did not fit the facts of the case. They wrote in their judgment: "The appellant was the last known adult to see the deceased alive, and the first known adult to see her dead. His clothing was found upon examination to be spattered with blood in a way which was consistent with him being her attacker. The clothing of others who went to the aid of the deceased was not similarly spattered."
Billy-Jo had lived with Jenkins, his wife, Lois, and their four natural daughters, as a foster child since 1992. It was expected that in due course they would adopt her. On the afternoon of her death, Jenkins had been with his two eldest daughters, aged 10 and 12. Both girls were questioned by the police about the day's events. The three judges rejected Mr Scrivener's appeal that the police embarked on a deliberate campaign to influence the children and taint their evidence.
The judges noted that in the initial stages of the police inquiry, Jenkins "repeatedly failed to reveal that he had been into his house about 15 minutes before the body was discovered", returning between two journeys. Moreover, they queried Jenkins's explanation for the quarter-hour after this visit. He said he had gone to buy white spirit, but found at the shop that he had no money and had to turn back; white spirit was later found at the house.
The judges said the explanation was "unusual in that he went without money by a circuitous route to buy an item that he did not need".
William Jenkins, Billie-Jo's natural father, said outside the court yesterday: "I think that Sion Jenkins has got the justice that he wanted. I hope he didn't expect anything else from this court or any other court in the land. You can't buy justice - not in this court."