The credibility of a key witness in a murder trial would have been "shot to pieces" if evidence that the victim was still alive had gone before the jury.
Terry Pinfold, from Essex, and Harry Mackenney, were jailed for life for murder in 1980.
But on Tuesday the men's lawyers argued that key evidence about the victim's whereabouts, collected during another police case, was never given to their defence team.
Edward Fitzgerald QC, for Mackenney, told the Court of Appeal that the police report was written more than three years after Terry Eve was supposed to have been murdered.
It said officers working under Scotland Yard's Commander Bert Wickstead had established Mr Eve was alive and living under an assumed name in west London.
Key part of appeal
Had that report been disclosed, it would have destroyed the evidence of the prosecution's star witness, Bruce Childs.
Childs had pleaded guilty to six murders and then turned Queen's Evidence, implicating Pinfold and Mackenney.
The evidence is a key part of a renewed appeal by the two men.
Their case has been referred back to the court by the Criminal Cases Review Commission, the watchdog which investigates possible miscarriages of justice.
In the 1970s, Pinfold and Mackenney - both ex-prisoners - were in business together making underwater diving equipment.
Convicted at Old Bailey
One weekend in November 1974, another former inmate, Terry Eve, who shared
their factory space in Dagenham, Essex, disappeared.
It was not until four years later that Childs, a former employee of theirs, claimed they were involved in murder.
As a result, the pair were convicted by an Old Bailey jury in November 1980 - Mackenney on four counts of murder and Pinfold on a charge of procuring Mackenney and Childs to murder Terry Eve.
Mackenney is still in jail serving a "whole life" tariff.
Pinfold was bailed, pending appeal, in September 2001 having served almost all of his
recommended minimum sentence.