The London Ambulance Service called police to an address in Brookside South at 1.37pm on Tuesday, June 21.
Officers were joined by paramedics from the London Ambulance Service and the London Air Ambulance.
When they arrived, they discovered a 37-year-old woman and a child, believed to be five years old, with stab wounds.
Both were pronounced dead at the scene.
The deceased are thought to be a mother and her daughter.
Detectives from the Met’s Specialist Crime Command have launched an investigation, and a 37-year-old man has been arrested on suspicion of murder.
Both the deceased and the arrested man knew each other.
“The whole community will be shocked and saddened to hear of this terrible incident,” said Chief Superintendent Sara Leach, policing commander for the North West, which includes Barnet.
“Our thoughts are with the families and friends of the woman and child who died, as well as the officers and paramedics who were the first to arrive at what was an extremely dangerous scene.”
Specialist detectives are investigating what happened, and a man is in custody. While they are keeping an open mind about what happened, I would like to reassure residents in the surrounding area that there is no evidence to suggest that anyone else was involved in this incident at this time.” I’d like to encourage anyone who witnessed or heard anything unusual earlier today or in recent days to come forward and speak with police. Your information could be crucial as the investigation progresses.”
Police can be contacted by dialling 101 and entering the reference 3590/21JUN.
Alternatively, it can be given anonymously to the independent charity Crimestoppers by calling 0800 555 111.