Michael Stone has lost a new bid to get his case referred back to the Court of Appeal.
Stone, 50, was convicted of bludgeoning mother and daughter Lin and Megan Russell to death with a hammer and attempting to murder Megan's sister Josie, now 24.
Today his lawyers asked two High Court judges for permission to challenge a refusal of the Criminal Cases Review Commission (CCRC) to back a fresh appeal.
Stone's counsel Mark McDonald argued that the CCRC had wrongly failed to investigate fresh evidence that undermined a confession Stone was alleged to have made in his cell to another prison inmate.
Dismissing the application, Lord Justice Hooper, sitting with Mr Justice Singh, ruled that members of the Commission had come to a decision they were entitled to reach.
Stone received three life sentences and has been told he must serve at least 25 years. The Russell family was attacked in Chillenden, Kent, in July 1996.
Stone was first convicted in 1998, but the convictions were overturned when witness Barrie Thompson admitted making up a story about Stone confessing in prison.
Stone was then found guilty at a second trial in 2001 on two counts of murder and one of attempted murder.
The re-trial relied on evidence of a cell confession from another prisoner witness, Damien Daley, who said he had spoken to Stone through a gap between a heating pipe and their cell wall.