The body of Maria Duque-Tunjano was found at a flat in Earl's Court Square.
She had been there for several days and a post-mortem examination found she died after a blunt blow to her head.
It is believed she was robbed of a quantity of cash during the assault.
The 48-year-old was a British national originally from Colombia and lived in Streatham.
She used the flat in west London where police found her for her work.
Detectives had linked her murder to an attack on another sex worker on January 18.
Police had been searching for Fraser, also known as Robert Aleem and Shia Robert Jackson, since the discovery of Miss Duque-Tunjano's body on Friday.
Scotland Yard said he was arrested on Tuesday night in the Leicester Square area of the capital and taken to a central London police station for questioning.
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