The Crown Prosecution Service is not expected to contest the appeal by Paul and Wayne Darvell, who were found guilty of killing Sandra Phillips, the manageress of a sex shop in Swansea, south Wales, in June 1985.
New evidence suggests that Wayne Darvell's confession, which formed the basis of the prosecution case, was unreliable and contained inaccurate information. Tests have shown police records of interviews with the brothers were made in notebooks issued several months later.
Two years ago, a BBC programme Rough Justice found witnesses who said Wayne Darvell was a fantacist and also uncovered evidence that other suspects were seen near the sex shop.
The brothers lost an appeal in 1987, but their case was re-opened after a petition from Justice, the British Section of the International Commission of Jurists. Yesterday, Anne Owers, the organisation's director, said: 'The case against them is now so weak we are very confident they will be released.'
Campaigners are certain to make renewed calls for safeguards for suspects in police stations and, in particular, for an end to convictions based on uncorroborated confessions.
The appeal coincides with the release of Justice's annual report showing a big rise in the number of cases it has been asked to investigate over the past year.
Of 847 cases it studied, 629 involved allegations of miscarriage of justice.