James Hanratty, the man hanged in April 1962 for the A6 murder, was probably guilty of the crime.
According to a British national newspaper DNA evidence has shown there is only a 1-in-2.5 million chance he was innocent.
A DNA sample was taken when Hanratty's body was exhumed outside London two weeks ago.
The 25-year-old was hanged for the murder of Mr Michael Gregsten and the rape and shooting of Valerie Storie.
The Daily Mailsays the evidence has been given to Hanratty's legal team and the news is said to be a blow to those who campaigned to prove his innocence.
Hanratty was not the initial suspect and was only arrested after cartridge cases from the murder weapon were found at a hotel where he had stayed the night before the murder. There was no forensic evidence against him.
Mr Geoffrey Bindman, solicitor for the Hanratty family, said: "The most they can prove is that Hanratty's DNA was similar or the same to that which was found on clothing at the scene of the crime. That leaves open the question of how it got there. Obviously one possibility was that it got there because he was the murderer.
"Another possibility was that it got there because the clothing came into contact with his DNA from some other sources. There are other sources and other possibilities because we know that at the time of the trial exhibits were handled freely because of course people did not know about DNA."
A Scotland Yard spokesman would not confirm or deny the Daily Mailreport.
Ms Storie, now 61, has said she believes Hanratty was guilty. But former dettective superintendent Roger Matthews who conducted the last re-investigation said there had been a miscarriage of justice.
PA