A sofa throw and towel caught light when a cigarette was not properly extinguished.
Shipley firefighters were called to Hallcroft sheltered housing complex on Church Street at 5.10pm.
Watch Commander Jonny Earl said an elderly woman had put a cigarette in a plastic bag which had melted and burnt papers beneath it.
A smoke alarm had alerted the warden who put the fire out and escorted the woman out.
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