Officers were called to the property in New Malden at around 9.30pm on Tuesday where they discovered the bodies.
A spokesman for the Metropolitan Police said: "A 43-year-old woman has been arrested on suspicion of murder and remains in custody. We are not looking for anyone else in connection with this incident."
The woman was being held for questioning in a south London police station.
A police officer was standing on the doorstep of three storey Victorian address in Thetford Road this morning.
Officers were seen leaving the property carrying evidence bags.
The ages of the children have not been released. Neighbours are reported to have said that the children were very young, and that the family moved into the area within the last nine month.
BBC London said several bags had been removed by officers from the property.