This is what the Wikipedia Article on the Whitehouse Farm murder says:
"New silencer evidence
Bamber's appeal at the Royal Courts of Justice was dismissed in December 2002.
Although all the grounds (except 11) were reviewed by the court, the reason for the referral to the Court of Appeal was ground 15, the discovery of DNA on the silencer, the result of a test not available in 1986. The silencer evidence during the original trial had come from a Mr. Hayward, a biologist in private practice, formerly of the Forensic Science Laboratory. He had found a "considerable amount of blood" inside the silencer; he had stated that it was human blood and that the blood group was consistent with it having come from Sheila. He said there was a "remote possibility" that it was a mixture of blood from Nevill and June.[190]
Mark Webster, an expert instructed by Bamber's defence team, argued that Hayward's tests had been inadequate, and that there was a real possibility, not a remote one, that the blood had come from Nevill and June.[191] This was a critical point, because the prosecution case rested on the silencer having been on the gun when Sheila was shot, something she could not have done herself because of the length of her arms. If she was shot with the silencer on the gun, it meant that someone else had shot her. If her blood was inside the silencer, it supported the prosecution's position that she had been shot by another party, but if the blood inside the silencer belonged to someone else, that part of the prosecution case collapsed.[192]
The defence argued that new tests comparing DNA in the silencer to a sample from Sheila's biological mother suggested that the "major component" of the DNA in the silencer had not come from Sheila.[192] A DNA sample from June's sister suggested that the major component had come from June, the defence argued. The court concluded that June's DNA was in the silencer, that Sheila's DNA may have been in the silencer, and that there was evidence of DNA from at least one male. The judges' conclusion was that the results were complex, incomplete, and also meaningless because they did not establish how June's DNA came to be in the silencer years after the trial, did not establish that Sheila's was not in it, and did not lead to a conclusion that Bamber's conviction was unsafe."
yet the Appeal notes state:
"478. On this information the CCRC decided that “the DNA results as they stood began to support
the theory put forward by the defence at trial”. They decided to take steps to see whether
the female DNA found within the moderator came from Sheila Caffell. To this end they
located Sheila Caffell’s natural mother and obtained a sample of her DNA. The evidence of
the testing of this sample was recorded as:
“The results of these tests were that…the DNA in the silencer could
not have come from Sheila Caffell”.