Hanratty, 25, was convicted of brutally killing a married man before he raped the victim's lover and repeatedly shot her, leaving her paralysed for life.
Home Office officials are understood to have concluded that Hanratty was innocent. This follows an unpublished police inquiry which concluded last year that he was the victim of a miscarriage of justice and that the murder was probably part of a wider conspiracy.
Michael Howard, the Home Secretary, is expected to announce within the next few weeks that he is to refer the case to the Court of Appeal, where the conviction is expected to be quashed.
The reappraisal of the case follows more than three decades of campaigning by members of Hanratty's family and his supporters. Many of the campaigners believe the real killer was Peter Alphon, who is alleged to have admitted to the crime on numerous occasions. There is also a string of evidence that links Mr Alphon to the murder, though in an interview with The Independent he protested his innocence.
Hanratty, a petty burglar, was convicted of abducting Michael Gregsten, 36, and his mistress Valerie Storie, 22, at gunpoint from a cornfield at Taplow, near Maidenhead, in Berkshire, in August 1961. The lovers were forced to drive about 60 miles to a lay-by on the A6 near Bedford, known as Dead Man's Hill. At the end of the two-hour trip Mr Gregsten, a research scientist, was shot dead. Miss Storie was then sexually assaulted before being shot repeatedly at close range.
Hanratty was arrested in Blackpool two months later, on 9 October. Reports at the time said this followed the "amazing" identification of Hanratty by Janet Gregsten, the wife of the dead man, who saw him on a London street and her "intuition" told her he was the killer even though at that stage he was not a suspect.
He was convicted largely on the identification evidence of Miss Storie, despite her only seeing her assailant for a few seconds and only identifying Hanratty in a second line-up. She later admitted that her memory of the attacker was fading.
On the morning of his execution at Bedford jail Hanratty wrote to his family, insisting he was innocent and asking them to clear his name. His brother, Michael Hanratty, 58, who has fought for the past three decades for the case to be taken to the Court of Appeal, said: "The day before Jimmy was hanged he said: `I'm dying tomorrow but I'm innocent. Clear my name.' This is what we need to be able to do."
At first, the campaign was headed by Hanratty's father, also named James, who toured Britain showing a film in an effort to clear his son's name. He handed out leaflets to the public outside the House of Commons proclaiming his son's innocence.
But any pardon will come too late for Mr Hanratty senior, who died 20 years ago. The campaign was taken up by Hanratty's mother, Mary, who is now suffering from Alzheimer's disease, along with Michael, and his other brothers, Peter and Richard.
Other campaigners included two lawyers, John Justice and Jeremy Fox, who became convinced of Hanratty's innocence. Four books and a number of television programmes, including two by Yorkshire Television, have also been instrumental in having the case reopened.
In the 1992 programme, Hanratty: Mystery of Dead Man's Hill, a documentary for Yorkshire, the film-maker Bob Woffinden called for DNA tests to be carried out to establish the true identity of the murderer.
These were eventually carried out at the beginning of 1995, by comparing semen found at the scene of the crime with DNA from Hanratty's exhumed body. But unfortunately the DNA retrieved was not of good enough quality to obtain a result.The campaign has gone on ever since.
One of the most implausible aspects of the case was the acceptance that Hanratty, a city dweller, should by chance come across the couple in a cornfield and carry out a random killing.
It emerged after his execution that Hanratty also had a good alibi. Fourteen witnesses came forward to back up his claim that he was in Rhyl, North Wales - 250 miles from the scene of the crime.
Doubts about the identity of the killer were dismissed, however, by Mr Alphon. In an interview with The Independent, in which he denied his own involvement, Mr Alphon set out his own theory. He said that Hanratty was a "psychopath" who had been hired by the wife of the dead man and her lover. Earlier this month, Mr Alphon sent a letter to the Home Secretary, saying "...the nightmare has persisted through four decades of controversy and speculation surrounding the case".
He added: "My victimisation both at the hands of the police and my defamers in the media dates from when Scotland Yard quite unjustifiably caused my name to be blazoned across the headlines ..."
But growing concerns about the safety of the conviction brought a Scotland Yard inquiry headed by Detective Superintendent Roger Matthews. He completed his report last year and is understood to have concluded that Hanratty was wrongly hanged.
He was executed in April 1962, but doubts about his conviction played a significant role in the decision by MPs to abolish capital punishment in 1965.
Geoffrey Bindman, the solicitor who represents the Hanratty family, said: "We have been asking for a referral to the Court of Appeal with the new evidence for more than a year. The police officer appointed to look into the case came up with a view that he was innocent. Clearly, his conviction should by quashed by the Court of Appeal.
"There are a lot of people who say bring back hanging. The fact that such a well-known hanged person turns out to be innocent will act as a powerful example against capital punishment."
The Home Secretary will have to announce his decision on the Hanratty case by the end of March when the new independent Criminal Case Review Commission takes over the role of resolving claims of miscarriage of justice from the the Home Office's C3 department. It would be unusual for a Home Secretary to go against the advice of his officials in such cases.
Crime of the century, page 8
The 35-year fight
22 August 1961: Michael Gregsten murdered; Valerie Storie assaulted and shot.
17 February 1962: James Hanratty convicted of murder at Bedford Crown Court.
4 April 1962: Hanratty hanged.
1967: Peter Alphon "confesses" to killing in Paris, but later denies it.
1971: Paul Foot's book Who Killed Hanratty? published.
1992: Television programme Hanratty: Mystery of Dead Man's Hill broadcast.
1995: Inconclusive DNA tests of Hanratty carried out.
1996: Police inquiry concludes Hanratty was innocent.