A 19-year-old man was arrested at the scene, Russell Square in the heart of the city, after being tasered by officers.
The woman was treated by paramedics at the scene but pronounced dead. No details were released about the condition of the other victims.
"Early indications suggest that mental health is a significant factor in this case and that is one major line of inquiry," London Metropolitan Police Assistant Commissioner Mark Rowley told reporters.
"But of course at this stage we should keep an open mind regarding motive and consequently terrorism as a motivation remains but one line of inquiry for us to explore."
A large police presence was deployed to area, which is close to the British Museum and the University of London, following the attack.
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