A woman is being held by police on suspicion of murdering her four-year-old daughter and twin sons aged three.
Tania Clarence, 42, cared full-time for the three children, who are understood to have suffered from a life-limiting genetic condition, while their father Gary worked as a director at City bank Investec.
Police were called to their large semi-detached home in New Malden, south London, where they found the bodies last night
Officers are not looking for anyone else in connection with the deaths.
A Scotland Yard spokesman said that a 42-year-old woman was taken to hospital for treatment to minor injuries before being discharged and arrested.
An elder child, thought to be around seven or eight years old, was also living at the house but was in good health.
Mr Clarence, who trained as a solicitor before going into banking, was not at home at the time of the deaths but is understood to have been informed about the tragedy.
Originally from South Africa, the family moved to the wealthy suburb around a year ago and carried out a major refurbishment of the home, which included installing a lift.
Police have not given a cause of death for the three children, but said post-mortem examinations will be carried out in due course.
A poignant makeshift memorial with two teddy bears, bouquets of flowers, pot plants and a child's skipping rope were laid on the driveway of the house by a police officer.
Uniformed officers were standing guard on the doorstep while scenes-of-crime officers were seen leaving the property carrying evidence bags.
Officers said they are trying to speak to members of the extended family to find out what happened.
Neighbours spoke of their shock at the news of the children's deaths, describing the family as "really, really lovely people".
Michele Bacchus, 38, a mother of two who lives nearby in Thetford Road, said two "very, very upset" relatives of the Clarence family had asked to use her toilet last night , around an hour after four police cars and an ambulance had appeared in the road.
The women, one in her 30s and the other in her 50s, said they had come from Cobham, Surrey.
One had a South African accent and the other was too upset to speak, Ms Bacchus said.
"We heard a commotion and we saw lights and four police cars came up and one ambulance and a few other cars.
"We came outside to see what was going on and two other neighbours came out," she said.
"A little while later my partner was outside having a cigarette and two women came up and asked if they could use the lavatory. One was fairly young and very, very upset, she could not speak."
Retired nurse and health visitor Joy Devis, 86, said that the news of the children's deaths was a "huge surprise and shock".
"They are a delightful couple, they seemed to be very happy," she said.
"Their children were super, lovely children. They were very happy, there was a very nice atmosphere there."
Ethel Winstanley, who lives opposite the couple, said she met them last summer and congratulated them on the "transformation" of the house in Thetford Road following its refurbishment.
She said: "We went across to say 'congratulations, you have made the street look wonderful'."
Mr Clarence has worked at Investec, an international banking and asset management firm, for 15 years.
He specialises in healthcare and leads a team which advises clients on buying and selling companies, raising money and strategic reviews.
The company said in a statement: "Gary Clarence is a valued colleague and has worked with us for many years.
"We do not know the facts at this time but our thoughts are with the Clarence family.
"We are doing all that we can to help Gary and his eldest child and ask that their privacy is respected."
A Scotland Yard spokesman said: "The three children - a girl aged four and two boys aged three - were pronounced dead at the scene. Next of kin have been informed.
"The woman, aged 42, was taken to hospital for treatment to minor injuries and later discharged.
"She was arrested on suspicion of murder and taken into custody at a south London station where she remains.
"The Homicide and Major Crime Command is investigating and an incident room has opened in Sutton under Detective Chief Inspector Diane Tudway.
"Detectives are not looking for anyone else in connection with this incident."