The victim, believed to be in her late thirties, died in the gutted flat on the ground floor of council-owned Aylwin Court, Granary Way, Horsham.
Horsham fire-fighters were called to the scene just after midnight.
Crews fought their way through the flames and found the woman's body.
Most of the residents had evacuated the building by the time emergency services arrived.
People on the top floor were advised to stay upstairs on balconies away from the flames as dense smoke billowed up the stairwell of the building.
Lisa Kingshott, 26, told the Argus: "I was asleep when I heard banging on the door. A neighbour told me a flat below was alight.
"All I could think about was my little girl Jordan, who is three and a half. I woke her up and carried her outside wrapped in blankets.
"I just had my dressing gown on, with a coat over it and an old pair of trainers."
Lisa, an accounts clerk, added: "We didn't get back into the flat for about three hours and because of what happened, with the noise and everything, we have had little sleep.
"I knew the lady who died to say hello to. She seemed very nice."
Rachel Price, who lives on the floor above the gutted flat, escaped with her three-year-old daughter Megan.
She said: "I grabbed her and ran downstairs. We were alerted early enough that the smoke was not a problem for us. But you could feel the heat coming from the burning flat."
Top floor resident Mick Hoskins and his pet bull terrier Woods stayed with a neighbour on his outside balcony while the blaze was brought under control.
He said:"Firemen told us it was safer to stay where we were as long as we kept the front door closed.
"The top landing was full of black-greenish fumes. You couldn't see three feet in front of you."
Police and fire experts were today investigating the cause of the blaze, which is not thought to be suspicious.
The identity of the woman is not being released until next of kin have been traced.
The flat was badly damaged by the blaze and the rest of the building suffered serious smoke damage.
. Two dogs were carried to safety by Crawley firemen last night after a motorbike stored inside a house caught alight.
Neither animal was hurt and no people were in the Partrington Close, Bewbush, house at the time.
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