The court exploded into uproar when Lord Justice Watkins reached the conclusion of the 57-page judgment after reading aloud for almost two hours.
Two of the men, Michael Davis, 26, and Raphael Rowe, 25, grabbed the dock rail and screamed obscenities before being bundled away by prison officers.
Rowe's sister, Joanne Rowe, was also hurried from the well of the court after screaming at Lord Justice Watkins: 'I hope you drop dead when you retire.' The judge, who is deputy Lord Chief Justice, retires this week.
In dismissing the appeals, following a hearing last month, Lord Justice Watkins, sitting with Mr Justice Leonard and Mr Justice Scott Baker, said there was no basis for saying there was 'even a lurking doubt' about the convictions.
He added: 'On the contrary, the case against them all was, and remains, a formidable one.'
Davis, Rowe and a third man, Randolph Johnson, 28, all of Afro-Caribbean origin, were jailed for life at the Old Bailey in March 1990 for the murder in December 1988 of Peter Hurburgh, a hairdresser, in Warlingham, Surrey. The murder took place on the same night as a man was stabbed and a couple tied up during burglaries at houses in Oxted and Fetcham. The crimes were linked by their proximity to the M25.
Rowe and Davis, who lived in Sydenham, south London, were also sentenced to 15 years for robbery, grievous bodily harm and firearms offences. Johnson was sentenced to 15 years for robbery and grievous bodily harm. He was also convicted of a separate incident in which a woman was raped.
The men were convicted largely on the basis of evidence from three white men who lived in the same house as Rowe and Davis. They admitted stealing a car used in the crimes, handling stolen property and possessing firearms, but were never charged.
Other evidence linked the men to some of the stolen property while a girlfriend of Rowe's said he had been away from the house during the night. A girlfriend of one of the white men also described Rowe and Davis arriving home early in the morning after the crimes and admitted being given a plant, taken from one of the houses, by Davis.
During the appeal, it was argued that inconsistencies in the accounts of the witnesses, particularly over timings, the lack of scientific evidence and the fact that the victims described the assailants as two white men and one black man created doubts about the convictions.
Lord Justice Watkins said the jury's verdict had been correct. Inconsistencies and mysteries in the case had been before them and they had decided which parts fitted the jigsaw.
'There is no dispute . . . the judge fully and fairly summarised the evidence, taking particular care to point out . . . anomalies and discrepancies. He was also careful to try to help the jury as to the relative weight they might think it right to place on material which was inconsistent with evidence from another source.'
Afterwards, lawyers for the men said they would take the unusual step of making an immediate application to the Home Secretary for the case to be referred back to the Court of Appeal. Normally, such applications are only made if there is considered to be fresh evidence.
Nigel Leskin, solicitor for Rowe, said the judgment was 'an absurdity in logic and fact'.
Valerie Davis, the sister of Davis, said the court was racist. She added: 'The campaign has now stepped up 100 per cent. We will fight and fight and fight and no matter how long it takes we will succeed.'