Jamie-Leigh Kelly, 31, left the centre for vulnerable mothers and children in north-west London on Tuesday with her three-year-old daughter and newborn baby boy, the Metropolitan Police said.
The children were found at an address in Harwich on Sunday.
The youngsters were taken into police protection and then to hospital as a precaution.
A 31-year-old woman was arrested later on Sunday after attending an east London police station and was also taken to hospital for precautionary checks, a Scotland Yard spokesperson said.
They added: “We are no longer appealing for information about the whereabouts of Jamie-Leigh Kelly.”
A 63-year-old woman was arrested at the address in Essex on Sunday on suspicion of child abduction, assisting an offender and perverting the course of justice.
She remains in custody at an east London police station.
Two other people have been charged as part of the investigation, the Met said.
Ashley Hawkins, 52, of Alex Guy Gardens, Dagenham, and Jordan Hardy, 30, of Connor Road, Dagenham, are due to appear at Southend Magistrates’ Court in Essex on Monday, charged with two counts of child abduction.
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