Victoria Gayle, 32, pleaded guilty at Kingston Crown Court to preventing the lawful and decent burial of a body.
The offence, which relates to a son born in 2004, only came to light after the death of Gayle's young daughter last year.
Investigations are under way into possible failings by the police and local authorities.
There is no record of any official agency having seen Gayle's son after he left hospital with her in February 2004, the BBC understands.
He is thought to have died when he was 10 to 15 months old.
On 31 May this year homicide detectives found a boy's skeleton at the home of Gayle's parents in West Hendon, north London.
The body had been placed in a box and wrapped up.
Gayle had been arrested a day earlier on suspicion of murder.
Following the discovery of the body, detectives re-arrested Gayle on suspicion of preventing a lawful and decent burial.
An investigation had started following a case review after the death of Gayle's two-year-old daughter in 2015.
She had died after swallowing a battery at the home of Gayle's parents.
The BBC understands that, over several years, Gayle told official agencies that her son had moved away, but that the agencies failed to establish whether or not this was true.
During court proceedings in 2014 Gayle had provided a statement that said her son had gone away with his traveller father.
But her son had already died and his father was not a traveller.
Tests, which are attempting to show how the baby died, are ongoing.
Three other people arrested in connection with the investigation remain on police bail.
Gayle has pleaded not guilty to two counts - perjury and perverting the course of justice - which have been left to lie on file.
In a statement, the Independent Police Complaints Commission (IPCC) said it was directing an investigation by the Met's Directorate of Professional Standards.
"The IPCC investigation is to establish what interaction, if any, officers from the MPS [Metropolitan Police Service] had with the family of the child and whether there were any missed opportunities, either before or after the death."
A serious case review, which started in October, is looking at the circumstances relating to both deaths.
A Barnet Council spokesperson said: "The death of any child is tragic and we are working with Barnet Safeguarding Children's Board to provide information for their Serious Case Review and to establish any learning from our involvement with the family."
Gayle was bailed ahead of sentencing at Kingston Crown Court on 3 February 2017.
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