Retired barmaid Anne Fowler, aged 79, died from burns and smoke inhalation after a discarded cigarette or a match sparked the blaze at her house.
Her body was discovered by the emergency services after her son Stephen arrived at the property, in Edison Road, Beechdale, to find thick smoke billowing at 10am on November 5, last year.
He rang 999 for help.
The pensioner, who was a smoker and had difficulty walking, was found lying dead on a sofa.
Black Country Assistant Coroner Dr Andrew Thompson, who recorded Mrs Fowler's death as accidental, said he will ask the Government to look into ensuring the dust covers are removed from smoke alarms.
West Midlands Fire Service investigator Watch Commander Jason Dean told the hearing at Smethwick Council House that although the detectors were heard going off by Mr Fowler and the firefighters, the plastic cover may have resulted in a delay in the pensioner being alerted.
The blue cover was installed while work was being carried out on the premises by the owners Beechdale Community Housing Association.
Mr Dean said: "It was evident from examination of the detector that at some stage it had sustained heat damage as it fell off the ceiling onto the floor and that would have taken some time to occur.
"It is evident that the smoke detectors were going off, but one of them didn't pick up any smoke until it was too late."
He said: "The seat of the fire was in either the furniture or Mrs Fowler's clothing. There was no other fire source in the room other than from cigarettes or matches."
Mr Dean said since Mrs Fowler's death the housing association had checked all its sites to ensure covers were removed after the completion of any repairs.
He said the covers did carry warning labels, advising that they should be removed.
Coroner Dr Thompson said: "I will write to the Home Office to ask them to look at the legislation relating to housing associations and to the installers of smoke alarms to ensure that these covers are removed before people are given occupancy of premises.
"Hopefully that will go some way to prevent similar deaths in the future."