His first challenge to his conviction was rejected by the Court of Appeal in July 2002.
Yesterday’s proceedings follow a decision by the Criminal Cases Review Commission, an independent body which investigates possible miscarriages of justice, to refer George’s case back to the Court of Appeal after a “thorough and intensive review”.
The prosecution claimed at trial that the residue linked him to the shooting, but his defence team said the particle was completely unreliable as evidence.
George’s sister, Michelle Diskin, was one of the dozens of people present in the public gallery for the hearing.
Her brother was sentenced to life in July 2001 after being found guilty by a majority of 10 to one at his Old Bailey trial.
William Clegg told the court that, during his trial, George, who has “learning difficulties” and intellectual functioning in the “borderline range”, was assisted in following the proceedings by a clinical psychologist, who sat with him in the dock.
The same psychologist was present in the dock with George yesterday, along with three security officers.
George, who lived about 1km from Ms Dando’s home, has always denied being her murderer.
During yesterday’s hearing, a man stood up in the public gallery and shouted at the judges that they were being misled because counsel did not understand the evidence relating to the particle. He left the court with security officers.
At the start of the hearing, Lord Phillips said the court had received correspondence about the appeal but had not read it because it should not have been sent. “Justice in this country is administered in public and it is important that the public should see or hear any submissions made to the court through the lawyers conducting the process,” he said.
Lord Phillips also said that he and his fellow judges had not seen either of the recent documentaries about the case.