Police were called to the address on Friday at 8.50pm after reports that two women had been seriously injured and pronounced them dead at the scene.
"This was a devastating attack on two women in their homes".
Formal identification of the victims has yet to take place, but police are confident they know the identify of the women, whose next of kin have been informed.
No arrests have been made but enquiries are ongoing.
Scotland Yard said Joshua Cohen, 27, was arrested in connection with the killings of the victims, aged 33 and 66.
Police are appealing for information on his whereabouts.
Cohen was last seen wearing a red Nike hooded top with a white logo on the chest, dark grey pants or tracksuit bottoms and white trainers.
Police described Cohen as white, 5ft 9ins tall with short cropped hair and a short beard/stubble.
He was also wearing white trainers and dark grey pants or tracksuit bottoms.
Police warned people not to approach Cohen but to call 999 if they see him. Detectives added that he had recently shaved his head and eyebrows.
Detectives are hunting for Cohen who has mental health issues including paranoid schizophrenia.
Officers from the Met's Homicide and Major Crime Command are investigating.
The man was arrested after he was spotted by a member of the public following a police media appeal.
Police have urged anybody who saw anything in the area on Friday night to get in touch with investigators immediately.