At 9.34pm on Thursday, 19 August, officers attended an address on Ashbridge Street, NW8 after concerns were raised for the wellbeing of the occupants.
Officers attended and searched the property and found a 45-year-old woman who had suffered a knife injury. She was pronounced dead at the scene.
Enquiries are underway to trace next of kin. Formal identification awaits.
At 2.15am on Friday, 20 August, police were alerted by the London Ambulance Service to reports of a man with a knife injury at a property in nearby Jerome Crescent, NW8.
Officers attended with paramedics who confirmed that the 59-year-old man was deceased.
Their next of kin have been notified and are being supported by specialist officers. Formal identification awaits.
Post-mortem examinations will be scheduled in due course.
There has been no arrest at this time. A homicide investigation, led by Detective Chief Inspector Wayne Jolley, has been launched.
DCI Jolley, said: “Firstly, our thoughts are with the families of the victims. We can only begin to imagine what they are going through.
“At this early stage we are retaining an open mind concerning motive, but at this stage we are treating these crimes as linked.
“We are very keen to hear from anyone who saw anything suspicious around Ashbridge Street, or Jerome Crescent overnight. No matter how small or insignificant you think your information might be, please do get in touch.”
Police commander for Westminster, Detective Chief Superintendent Owain Richards, said: “We know that local residents will be shocked and troubled by this news.
“Crime scenes are in place in Ashbridge Street and Jerome Crescent and additional police resources and patrols have been deployed throughout the area to provide local reassurance.
“Anyone who has concerns is encouraged to approach patrol officers. To pass on information please call 101.”
Anyone who saw anything suspicious should call 101, giving the reference 7227/19AUG.