Richard Taylor is writing to the Prime Minister to ask for the inquiry into "how the system has failed so badly in this case", the Damilola Taylor Trust said.
It comes as Ricky Preddie, one of the 10-year-old boy's killers, was recalled to jail for a second time just 16 days after being released.
Preddie, who was jailed for eight years in 2006 for the manslaughter of the 10-year-old, was recalled to prison last night for breaching the terms of his licence after he entered an exclusion zone in Southwark, south London, and might have met former gang members.
He had been free for only 16 days after being released from Pentonville Prison in north London on January 25.
Gary Trowsdale, a spokesman for the trust, said Damilola's killers had never shown any remorse or reform and answers were needed about the handling of their case.
"The Taylor family, society at large, and also the boys themselves have been failed by the system and the academics that run it," he said.
"Now we are demanding answers and believe a public inquiry is the only way of getting them."
He went on: "Richard Taylor, supported by the Damilola Taylor Trust and other victim families, is writing to the Prime Minister calling for a public inquiry into how the system has failed so badly in this case.
"For the second time in 18 months, the boy has been recalled due to breaking the terms of his licence."
Mr Trowsdale added: "Once again, Richard was informed by the media before the probation service let him know."
The killing of Damilola was a hugely high-profile case, he said, "and, due to two bungled trials, it took £16 million in total to put the two boys into the prison system for four years".
"During this period there were many reported incidents of their continuing to break the law.
"There was never a hint of remorse or reform.
"The boys' age and association with other young offenders in the area saw them labelled as 'Peckham boys' and the area has suffered by association ever since.
"It has since been well-documented that the case was a landmark in the birth of a new wave of 'branded' youth gangs.
"Given the seriousness to society this case represented, the Taylor family and the DTT (Damilola Taylor Trust) have always maintained that the reform of the boys should have been essential before their release.
"They knew nothing but the life of the street and so would have little chance of creating new lives for themselves unless this was the case."
He went on: "Every young gang member walking the streets today knows the name Preddie.
"Now with the Taylor family being tortured again by the media interest in the boy being recalled a second time, we are calling on the Prime Minister to act."
Preddie, 24, was originally released in September 2010 but sent back to jail last March for breaking the conditions of his licence.
After being released again two weeks ago, he was arrested at an address in London last night.
On both occasions, he was recalled after being seen in Southwark, south London, and associating with gang members - both against the terms of his release.
Harry Fletcher, assistant general secretary of the probation union Napo, said: "He was recalled yesterday following information received from the police that he had entered the exclusion zone and may have been in contact with banned persons - former gang members.
"This is his second recall for the same breach of trust.
"It will be treated seriously by the authorities and he could now serve as much as another 14 months in custody."
Anyone recalled to custody will have their case referred within 28 days to the Parole Board, which will consider whether they can be released, a spokesman for the Parole Board said.
Preddie's sentence is due to end in May 2013.
A Ministry of Justice spokeswoman said: "The decision to release recalled offenders from custody is made by the independent Parole Board - the body solely responsible in law for determining whether or not prisoners should be released.
"Serious offenders released on licence are subject to a strict set of conditions and controls.
"Examples include a strict curfew and other restrictions on their movements, as well as frequent meetings with their offender manager.
"If they fail to comply with their licence conditions, they are liable to be returned to custody.
"They will also be managed under the statutory Multi-Agency Public Protection Arrangements (Mappa).
"Within Mappa, the police, Probation and Prison Services are required to work together to assess and manage the risks presented by the most dangerous offenders, in order to protect the public."
Damilola's death in November 2000 shocked the nation.
He had moved to Britain from Nigeria a few months before he was jabbed in the thigh with a broken beer bottle by a gang of youths as he walked home from the local library after school.
The youngster was found bleeding to death in a stairwell near his home in Peckham, south London, where local workmen tried to save his life.
Preddie, and his brother Danny, were convicted of manslaughter and jailed for eight years in October 2006.
Ricky Preddie, 13 at the time of the killing, was charged with his younger brother in 2005 when forensic evidence, missed at the time, revealed tiny blood spots and fibres.
Danny Preddie was released early in September last year after serving five years of his sentence.
PA
