The child, whose family was in contact with at least nine NHS professionals, was found dead in a flat on 8 March.
His 29-year-old mother was arrested for child neglect but died of an illness two days later, police said.
Westminster Council said there was "no suggestion" the boy had been "at risk of harm from neglect or abuse".
The boy is believed to have had serious developmental issues, an underlying serious health condition and had a history of being underweight.
A post-mortem examination could not fully establish the cause of the boy's death, Metropolitan Police said.
Westminster Council said the boy was not on the child protection register.
A serious case review has now been started into the boy's death.
The boy's three-year-old sister has been taken into care, police said.
Two health care trusts, Westminster City Council social services and a consortium of London boroughs providing health visitors were involved in the case.
"The review will look into several aspects of this complex and challenging case, many of which are still unclear at this early stage.
"When we have investigated the full circumstances that led to the baby's death, we will be able to determine if anything could have been done to help prevent it," he added.
Michael O'Connor, Westminster Council strategic director for children and young people, said: "The family was new to London and the council had arranged their housing.
"They were under the care of the health service, and social services were working closely with health professionals to help support them.
"Neither of the children were on the child protection register and there is no suggestion that they were at risk of harm from neglect or abuse.
"This is one of the saddest cases I have ever come across," he said.
'Serious health issues'
Nickie Aiken, the council's cabinet member for children and young people, said: "There were a number of serious health issues affecting the whole family and the baby had serious developmental issues.
"As far as I am aware, at least nine NHS professionals were working with the family and I hope that no stone will be left unturned to find out exactly why this child died.
"But I want to know why this child was being seen by nine NHS professionals and why things were not flagged up earlier."
The Metropolitan Police said the cause of death for the boy's mother had not been established, but it was believed to have been linked to an "existing illness". They said they were not treating her death as suspicious.
The matter has been referred to the Independent Police Complaints Commission.