Police were called to a property in New Malden, South London yesterday evening where they discovered the bodies, Scotland Yard said.
The three children – a girl aged four and two boys aged three – were pronounced dead at the scene.
It has been reported that the couple living at the property, named locally as Gary and Tania Clarence, had four children, but three suffered from genetic disorders and required the full-time care of their mother.
Speaking with the Mail Online, neighbours said of the couple: "They are very nice people and very, very decent.
"She [the mother] is such a lovely person - her life revolves around the children."
Police were called to the house in Thetford Road at 9.30pm yesterday, where the young family had moved in around a year ago after a major refurbishment, which included a lift for the children.
A 43-year-old woman was taken to hospital for treatment to minor injuries and later arrested.
A Met Police spokesman said: "Police were called at around 21:30hrs on Tuesday, 22 April, to three children found dead at an address in New Malden."
He added: "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."
Post mortem examinations were expected to be carried out on the three children later today to establish the cause of their deaths.