Tania Clarence, 42, is suspected of killing her four-year-old daughter and twin sons, aged three, who are all reported to have suffered from a life-limiting genetic condition.
It is understood the three children were severely disabled and were being cared for by their mother, while their father, Gary Clarence, was away. He worked as a director at City bank Investec.
Police were called to the family’s house in the south-west London suburb of New Malden, where they found the bodies on Tuesday night.
A Scotland Yard spokesman said the woman was taken to hospital for treatment for minor injuries before being discharged and arrested.
Officers are not looking for anyone else in connection with the deaths.
The family, originally from South Africa, moved to the house around a year ago and carried out a major refurbishment, which included installing a lift.
The three children were thought to be suffering from a disease called spinal muscular atrophy. An elder child, thought to be around seven or eight years old, who was in good health was also living at the house.
There were reports that the eldest child was on holiday with Mr Clarence in South Africa and the pair were yesterday on a flight back to the UK.
A neighbour who did not want to be named paid tribute to the family, describing them as “really, really lovely people” and said the parents are “a very, very lovely couple” who doted on their children.
She said: “They are very nice people and very, very decent. She is such a lovely person – her life revolves around the children.” The family are understood to have also received help from a nanny and carers.
Michele Bacchus, 38, a mother-of-two who lives nearby, said two “very, very upset” women had asked to use the toilet at her house on Tuesday night, around an hour after four police cars and an ambulance had appeared in the road. She said the women, one in her thirties and the other in her fifties, had said they were relatives of the Clarence family who had come from Cobham, Surrey.
One had a South African accent and the other was too upset to speak, she said.
“We heard a commotion and we saw lights and four police cars came up and one ambulance and a few other cars,” she said. “We came outside to see what was going on and two other neighbours came out.
“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. They were very upset. The younger one was in shock, they were both in shock.”
Another neighbour, Joy Devis, said: “They are a delightful couple, they seemed to be very happy. 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. She said: “We went across to say ‘Congratulations, you have made the street look wonderful’.”
Another neighbour, who did not want to be named, said she met the couple at a barbecue in the neighbourhood. She said: “They were very friendly. We were out last night dancing and when we came home there were police cars and ambulances outside.”
Mr Clarence, who trained as a solicitor before going into banking, is understood to have been informed about the tragedy.
Investec bank, where Mr Clarence works as the director of investment banking for healthcare, said the firm’s thoughts were with him.
A makeshift memorial of teddy bears, flowers, plants and a child’s skipping rope were yesterday laid on the driveway of the house.