At 13:37hrs on Tuesday, 21 June police were called by the London Ambulance Service to an address in Brookside South.
Officers attended with London Ambulance Service paramedics and the London Air Ambulance.
On arrival they found a 37-year-old woman and a child, believed to be aged five, with stab wounds.
They were both pronounced dead at the scene.
The deceased are believed to be mother and son.
An investigation has been launched led by detectives from the Met’s Specialist Crime Command and a 37-year-old man has been arrested on suspicion of murder.
The deceased and the arrested man were known to each other.
Chief Superintendent Sara Leach, policing commander for the North West including Barnet, said: “The whole community will be shocked and saddened to hear of this terrible incident.
“Our thoughts are with the family and friends of the woman and child who have died and also with the officers and paramedics who were first to arrive at what was an incredibly challenging scene.
“Specialist detectives are working to establish what took place and a man is in custody. While they are keeping an open mind as to what has taken place, I would like to reassure residents in the local area that there is nothing to indicate, at this stage, that anyone else was involved in this incident.
“I would urge anyone who saw or heard anything unusual earlier today, or in recent days, to come forward and speak to the police. Your information could be vital as the investigation moves forward.”
Information can be provided to police by calling 101 with the reference 3590/21JUN.
Alternatively, it can be provided to the independent charity Crimestoppers, anonymously, on 0800 555 111.