Bella Nicandro, 76, was attacked during a disturbance at her home in St Luke’s Road, Notting Hill at around 2.10pm on Saturday.
Mrs Nicandro was found inside the address suffering stab injuries.
Despite the best efforts of the emergency services, she was pronounced dead at the scene.
He appeared at Uxbridge Magistrates’ Court on Monday afternoon accused of Mrs Nicandro’s murder.
Cook, who was not known to the victim, will next appear at the Old Bailey on Wednesday.
Mrs Nicandro’s next of kin have been informed and are being supported by specialist officers.
Detective Chief Superintendent Owain Richards, in charge of policing Kensington and Chelsea, said: “I know the death of Bella Nicandro will have caused a great deal of shock and distress for the local community in Notting Hill.
“Officers will be carrying out increased patrols during the next few days to provide a reassuring presence.
“Anyone who has any concerns or wants to talk to police should approach one of the officers or ring 101, or 999 in an emergency.
“My thoughts are with Bella’s family at this difficult time.”
