Scotland Yard said they are are looking for 27-year-old Joshua Cohen in connection with the killings of the victims aged 33 and 66.
Police were called to an address in Golders Green Crescent, north west London, on Friday at 8.50pm after reports that two women had been seriously injured.
The women, who were known to the suspect, were pronounced dead at the scene.
Detectives are hunting for Cohen who has mental health issues including paranoid schizophrenia.
He is white male, 5ft 9ins tall with short cropped hair and short beard/stubble.
He was last seen wearing a red Nike hooded sweatshirt with a white logo on the chest. He was also wearing white trainers and dark grey trousers or tracksuit bottoms.
He has recently shaved off his hair and eyebrows.
A Scotland Yard spokesman said : “He has mental health issues including paranoid schizophrenia and should not be approached by members of the public. Any sightings of Joshua Cohen should be reported to police immediately via 999.”
Formal identification and most mortem examinations have yet to take place but police are confident they know the identify of the victims.
Their next-of-kin have been informed.