The 17-month-old, from Haringey, north London, died after months of being used "as a punchbag" and then having his back and ribs broken.
The tragedy has echoes of the Victoria Climbie murder in 2000, when eight-year-old Victoria died after care workers and police failed to save her.
Local MP Lynne Featherstone said the child, who she referred to as Baby P, had fallen through "safety net after safety net".
"The Children's Act was borne out of tragedy in Haringey after the death of Victoria Climbie," she said.
"Yet eight years after her death, the law created to stop this happening again has failed to prevent a similar tragedy in the same borough.
"Baby P should have been at the centre of all decision making.
"We must therefore have a fully independent investigation by the Children's Commissioner into what went so terribly wrong."
Mor Dioum, director of the Victoria Climbie Foundation, set up to improve child protection, said: "This case is worse than Climbie. The signs were there but were not followed."
He also called for a public inquiry into the failings.
Councillor Robert Gorrie, Lib Dem leader of the opposition at Haringey Council, said: "The tragic death of Victoria Climbie, and the national reforms that resulted, should have stopped this happening again.
"With so many public organisations involved, why did one of them not act decisively to save this child?"
He added: "The public need independent reassurance and it is for this reason we need the Children's Commissioner to carry out a full and independent review of the case."
Sue Berelowitz, Deputy Children's Commissioner for England, said: "The maltreatment and death of any child by those who should care for them is a tragedy.
"Following Lord Laming's inquiry into the death of Victoria Climbie, the Government introduced stringent laws to enforce these measures.
"The safeguarding of children now requires the implementation of basic good practice - the child must be seen and listened to, chronological records kept, and agencies must share information.
"There are now clear lines of accountability for children's welfare and safety at the highest levels of local authorities, Primary Care Trusts, police and associated agencies.
"Everybody needs to examine their practice to ensure that no child dies or is seriously injured because of failures in the network. We must never be complacent when it comes to child safety."
In a statement after the verdicts, Sharon Shoesmith, chair of Haringey Local Safeguarding Children Board, defended the council.
She said: "The mother seemed to be co-operating with us: taking the child to doctors when he was ill, seeking help.
"In line with Government guidelines for such circumstances, we immediately set up an independent review into what happened and have acted on every recommendation."
Dr Jane Collins, chief executive of Great Ormond Street Hospital, which provided paediatric services to the child, said: "It is clear that more should have been done when the child was seen by a paediatrician two days before the child died."
The NSPCC's acting chief executive Wes Cuell said: "The horrific cruelty inflicted on this defenceless infant is shocking. One cannot imagine the excruciating pain and sadness this little boy suffered before he died."
He said spotting abuse was "fraught with difficulty", adding: "Abusers will lie about what they have done and cover up their crimes."
Mr Cuell said child protection workers were being "overwhelmed by the scale of child abuse" and needed support from the Government as well as the public.
The NSPCC said half of the children killed or seriously injured through abuse and neglect are babies less than a year old, while a further 20% are under the age of five.
On average, 47 pre-school children are killed every year, mostly by their parents or carers.
John Coughlan, chair of the Children's Inter-Agency Group (CIAG), said: "When an individual tragedy such as this occurs, it is vital that we all learn from any mistakes which were made, and redouble our efforts to protect children from harm.
"Systems for safeguarding children have improved over recent years, across all services, as the recent Joint Chief Inspectors' Report on Safeguarding showed, but there is more that we need to do.
"Agencies are working more effectively together, and more children are protected from harm.
"Sadly, though, we will never be able to protect all children from harm."
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