A royal pardon was an "inadequate remedy" for a "historic injustice" that led to a man being wrongly hanged in 1950 for killing his baby daughter.
Notorious serial killer John Christie confessed to the murders
The family of Timothy Evans is arguing in the High Court that his conviction should be formally quashed.
Mr Evans claimed at the time his neighbour John Christie committed the murders at 10 Rillington Place, London.
Three years later Christie, who helped convict Mr Evans, was found guilty of a string of murders at the address.
After Mr Evans, 25, was convicted of the murder of his daughter Geraldine in November 1949, a further charge that he murdered his wife Beryl was not pursued.
In the High Court on Tuesday, lawyers for Mary Westlake, the half-sister of Mr Evans, were asking judges to overturn a recent decision by the Criminal Cases Review Commission not to refer the case back to the Court of Appeal.
Relatives say the fact that he received a royal pardon in 1966, after two official inquiries, does not erase the stigma.
Edward Fitzgerald, QC told Mr Justice Collins and Mr Justice Stanley Burnton: "We are dealing with an historic and unique injustice of a man convicted on the perjured word of the serial killer who had actually committed the murder of both his wife and child."
He said the Criminal Cases Review Commission recognised the virtual certainty that if the matter was referred to the Court of Appeal it would quash the conviction.
But in March, a commission panel decided that, although there was a "real possibility" that the Court of Appeal would not uphold the conviction, it would exercise its discretion not to refer.
10, Rillington Place became a notorious address
It said the referral would bring "no tangible benefit to Mr Evans' family, the public interest or the criminal justice system".
The commission said the free pardon in 1966 with its publicity of Mr Evans' case as a miscarriage of justice, was "sufficient to establish his innocence and to restore his reputation."
Lawyers for Mrs Westlake of Melksham, Wiltshire, will point to the fact that an earlier inquiry, although concluding that Mr Evans probably did not kill his daughter, did not declare him innocent.
There was also the "devastating" conclusion that, on the balance of probabilities, he had probably killed his wife, although he was not convicted.
Both had been strangled in a bath house at 10 Rillington Place, Notting Hill, west London.
The address later became notorious as the home of serial killer John Christie, who was a downstairs neighbour to the Evans family.
Mr Evans, originally from Merthyr Vale, south Wales, was hanged on 9 March 1950 after an appeal was dismissed.
It was three years before Christie - a central prosecution witness in the case against Evans - emerged as a serial killer and was himself hanged.
The remains of Christie's wife Ethel and those of five other women were found in the house.
At his trial, Christie admitted that he had murdered Mrs Evans and later indicated that he may have been responsible for murdering Mr Evans' daughter.