Michael Davis, Randolph Johnson and Raphael Rowe have had their cases referred back to the Court of Appeal by the Criminal Cases Review Commission, the body responsible for reviewing suspected miscarriages of justice.
Mr Justice Smedley yesterday refused the application. The men, who have so far served 10 years in jail, will now continue their sentences.
Family members and campaigners were "bitterly disappointed".The judge, however, indicated the full appeal could be heard before the end of this year.
Michael Davis's brother, Lloyd, said: "It is extremely frustrating especially when you know Michael is innocent. There is still a long way to go ...justice will be done. Clement Davis, Michael's father, was "extremely disappointed".
The three black men were jailed for life in 1990 for crimes which left one man dead, but they have always vigorously protested their innocence.
They were jailed at the Old Bailey for a series of attacks in December 1988, including murdering Peter Hurburgh.
He was dragged from his car at gunpoint with his homosexual lover, tied up and beaten - which led to him having a fatal heart attack.
The case mainly rested on three suspects turning prosecution witnesses. Direct forensic evidence linking the men to the crimes is absent, with witnesses describing attackers as male, two white and one black. Their case was dismissed by the Court of Appeal in July 1993.Reuse content