Locals said they were alerted to the fire by shouts of the victims sleeping inside the complex.
"At around 3.45 AM when I came out of my house after hearing those screams, I saw flames coming out of window panes of the building with people shouting from the windows," Ranjit Hazra, a resident of the area, said.
Shopkeepers and locals said that lack of adequate fire-fighting mechanism and exit routes were responsible for the 19 deaths in the fire.
Another shop owner Dipak said the entire staircase of the market complex was blocked by goods belonging to shops.
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State fire services minister Javed Khan said most of the people killed were either labourers working in the market complex or shop-owners who slept in their shops in the night.
Khan's views were endorsed by the governing body members of the market complex.
"Those who have died are mostly labourers, but a few of them were also shop owners. There was only one proper exit. There is an emergency exit but it has not been used for the last 10-15 years," Sushanta Ghosh, vice-chairman of the market, said.
According to Khan, about 200 shops situated in the ground and the first floor were gutted.
The five-storeyed building mainly housed shops and offices.
Ghosh said the fire first spotted on the ground floor worked its way up through the floors.
West Bengal Chief Minister Mamata Banerjee has ordered an inquiry into the incident.