According to the Fire Brigade, the fire which erupted a few minutes before midnight was under control by around 3:00 a.m. local time on Monday, but firefighters would continue to "damp down" the site in order to prevent any re-ignition.

There were no immediate reports of any casualties or cause of the blaze.

The London Fire Brigade said on Twitter in an earlier statement that the first three floors and roof of a building within the market were alight.

"The Brigade's 999 Control Officers have taken multiple calls to the highly visible blaze and people are asked to avoid the area," it said on Facebook.

This is the second major fire incident in London in recent weeks. On June 14, a fire tore through the Grenfell Tower residential building, killing at least 80 people.

Cheap materials used to refurbish the tower was cited as the reason for the Grenfell inferno, according to a report published in The Times.

The 24-story building block with 120 apartments was home to many Muslim residents.

Reports said a lack of suitable equipment, low water pressure and radio problems hindered the response to the Grenfell Tower disaster.