Michael Mansfield QC, representing Raphael Rowe and Michael Davis, two of the three serving life sentences for murder, robbery, violence and firearms offences, said the prime evidence against the men came from accomplices.
There was no scientific evidence, such as blood, fibres, soil or fingerprints linking them with the crimes. Despite the fact that the three men were black, all the victims described two white men and one black man.
Rowe, 25, Davis, 26, and Randolph Johnson, 28, were convicted at the Old Bailey in March 1990 of incidents on 15 December 1988 in Surrey, including the murder of a hairdresser, Peter Hurburgh, and two burglaries.
At the outset of yesterday's hearing Lord Justice Watkins, sitting with Mr Justice Leonard and Mr Justice Scott Baker, rejected an application from Mr Mansfield to order the Crown to disclose who had received pounds 25,000 reward money in the case.
Mr Mansfield suggested that some of the money had gone to three white male accomplices and two women associated with the men, who had all given evidence for the Crown at the original trial: 'One or more of the accomplices were certainly involved in the offences. None was charged with anything. Two of them thought they might be charged; another claimed he was told he would not be charged.'
The court also rejected an application by Mr Mansfield for the disclosure of a report of a police inquiry into a 38-minute interview between one of the accomplices, Norman Duncan, and detectives, which was not recorded. The officers insisted it was a 'background chat'.
Mr Mansfield said the only fingerprints discovered belonged to Mr Duncan and another of the accomplices, Mark Jobbins, on a car at the murder scene. Mr Duncan, Mr Jobbins and the three convicted men had all shared a house in south London.
'There is a mystery about this case. It was a mystery conceded by the Crown to the jury . . . to which there is no answer,' he said. 'There is an underlying bedrock of doubt.'
Despite evidence against the accomplices, they had not been charged with any crime. Mr Mansfield said they had handled the stolen property, had access to weapons, one of the descriptions fitted Mr Duncan and they had disposed of the stolen cars.
He said that on Monday the Crown disclosed to the appellants pages from a police officer's notebook recording an interview with one of the victims, which also mentioned two white men and one black man. Its sudden emergence could amount to 'a material irregularity'; it had not been disclosed at the original trial.
The hearing was adjourned until today.