Detectives are looking to speak to Lee Peacock, who was seen at North Wembley station on the evening of 19 August.
On that same evening, police were called to an address in Ashbridge Street, Westminster, at 9.30pm, where 45-year-old Sharon Pickles was pronounced dead.
At 2.15am on Friday 20 August, 59-year-old Clinton Ashmore was pronounced dead at a nearby address in Jerome Crescent.
The Metropolitan Police have said both people died from a stab wound to the neck and the two incidents are being treated as linked.
An appeal was issued on Friday for information about Mr Peacock, with officers saying that they wanted to locate and to speak to the 49-year-old about the murders as they believe he knew both Ms Pickles and Mr Ashmore.
“I am appealing today for further information about the whereabouts of 49-year-old Lee Peacock, who we need to speak to urgently about the murders of two people in Westminster,” Detective Superintendent Luke Marks, of the Specialist Crime Command, said in a statement.
“I am asking anybody who sees Lee to call us immediately on 999. I would urge members of the public not to approach him, but instead to call police as soon as possible.
“I believe Lee could have important information about the deaths of two people whose bodies were found at two properties in Westminster on the 19 and 20 of August.”
Information on the murders can also be provided by calling police on 101 or by contacting Crimestoppers anonymously on 0800 555 111.
The Met also noted that the victims’ families had been informed and were being supported by specially trained officers.
“At this early stage we are retaining an open mind concerning motive, but we are treating these crimes as linked,” Mr Marks said.
He added that a £20,000 reward was being offered for any information that leads to the conviction of the individual responsible for the murders.
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