Linah Keza, 29, was stabbed, the Daily Mirror reported.
A suspect was being questioned Thursday, police said, describing him as a 38-year-old man. Family members said Keza had been in an abusive relationship.
Herbert Muhire, a cousin, spoke to the Mirror from Rwanda.
"The police were aware of the death threats placed on Linah and she had a panic button in the house," he said. "Having a child, they were in close contact, and she had wanted to make up and get married."
The Metropolitan Police said officers had had previous contact with Keza and the suspected killer. A spokesman said the case had been referred to the Independent Police Complaints Commission for review.
Keza's brother, Jack Hodari, used Facebook to send an angry message to the man he believes killed her.
"I curse the day you were born. Your name and everything about you is bitter," he wrote. "We know you are coward. I curse you and I declare that you'll know no peace and joy."
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