Officers attended the address in Brookside South, Barnet, with London Ambulance Service paramedics and the London Air Ambulance just after 1.30pm this afternoon.
Upon arrival, officers 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 victims are thought to be a mother and a daughter.
The officers have now launched an investigation led by detectives from the Met’s Specialist Crime Command.
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.”
Metropolitan Police officers arrested have arrested a man on suspicion of murder.
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.