Sergey Koudriavstev, 48, was charged with two counts of the murder of the man aged 69 and woman aged 68 on Friday.
The pair were found at the flat in Adair Tower, Appleford Road, around 6.40am on Thursday after a man they knew contacted the Surrey Police.
Detectives from the Met were then called in to investigate their deaths, before bringing Mr Koudriavstev to a London police station for questioning.
A post-mordem will be carried out on the couple on Saturday.
The Met Police said in a statement: “Enquiries by the Homicide and Major Crime Command continue."
This investigation is led by the Homicide and Major Crime Command under DCI Rob Pack.
He said on Thursday: “This is an awful case where an elderly couple have been found dead in their home.
"My team are busy carrying out a number of enquiries included local CCTV footage review, house to house enquiries and forensic work but need to hear from those who have information.
"Do you live nearby? Did you see or hear anything suspicious? We need you to get in touch and speak with investigators as soon as you can.”