A Metropolitan Police spokesman said "the fire is being treated as suspicious" at a flat in Heston.
The woman died after she jumped from the second floor of the flat as she tried to escape from the blaze while a man was found dead inside the flat.
Another two men, aged 18 and 37, leapt to safety from the building.
They received multiple injuries which are said to be "not life-threatening."
Nearly 60 firefighters fought the fire, which took about three hours to bring under control.
Part of the second floor and half of the roof was damaged.
The fire was reported by police officers who were on patrol.
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