The first, second and third floors and the roof of the building were on fire, the brigade tweeted earlier, saying more than 70 firefighters and 10 fire engines were on the scene.
The cause of the fire was unknown and there were no immediate reports of any injuries or casualties.
London 's Camden Market had an incident of fire in 2008 when market storage areas and shops in the locality were set ablaze and adjoining houses were damaged. A major part of the market had then remained closed for several months.
In June, at least 80 people died in a devastating fire in London 's 24-storey Grenfell Tower.
Prime Minister Theresa May later said that 120 other high-rise buildings had failed fire tests.