Britton, 35, who was "injecting heroin daily" when she fell pregnant with Jayden Lee and Green, 33, were accused of killing their son by giving him the drug, which they both had on prescription.
After a three week trial at Bristol Crown Court, Green was convicted of manslaughter and causing cruelty to a child and jailed for nine years earlier in June.
The jury cleared Britton of manslaughter but convicted her of child cruelty and causing or allowing the death of a child. She was jailed for four years. The couple also have another son, who cannot be identified for legal reasons.
According to the 86-page report, published yesterday, a string of blunders were committed by doctors, hospital staff, police, social services and drug agencies in the lead up to the toddler's death, which started before he was born.
Despite the two drug addict parents regularly missing appointments, showing signs of relapse into heroin and cocaine use, falsifying tests and warning signs their son was being physically abused, the boy was not taken into care.
The report, parts of which were redacted, found a "lack of co-operation" between agencies and failures to detail concerns about the parents' conduct. It stated that not all lessons had been learned from a similar previous case.
"None of the professional involved with the family had foreseen the possibility of either child being given methadone by one or other of their parents," it concluded.
"There was a lack of challenge by practitioners across the range of agencies."
The report stated he had suffered two head injuries - one at seven weeks and one at 11 weeks - to which his parents said he had injured himself rolling off his changing mat.
Despite suggesting physical abuse, professionals believed the same explanation for both incidents from the parents, who started taking drugs as teenagers.
The boy also sustained injuries to his face at 21 and 23 months old and again the same explanations were given when he was seen by medical professionals.
Shortly before his death, police found a cannabis factory inside his parents' flat when they were arrested after coming home drunk from a pub with their children.
The report, which referred to Jayden Lee as "Child K" throughout, was highly critical of police for not using "their power to protect the children".
It added: "The only way that Child K's death would definitely have been prevented was if he had been placed away from his parents."
"The opportunity to do this was lost due to the failure to follow through on the initiation of care proceedings."
Social services have come under increased scrutiny since the death of "Baby P" in August 2007 after months of abuse and a series of failings by Haringey Council.
The toddler, now named as Peter Connelly, was just 17 months old when he died in Tottenham, north London, at the hands of his mother Tracey, her violent partner Steven Barker and his brother Jason Owen.
Last night Prof Ray Jones, the BSCB chairman, called on the Government to publish guidance on the testing of children for methadone.
He added: "This is a terrible tragedy with the death of a little boy, who was much loved, by the actions of those who cared for him."
A Bristol City Council spokesman said officials fully accepted the recommendations.
