Fifty firefighters and 10 engines managed to control flames which engulfed a building undergoing refurbishment in Great Portland Street.
London Fire Brigade was called to the scene at 12.43pm after taking more than 40 999 calls..
A number of gas cylinders were involved in the fire and a 25-metre exclusion zone was put in place.
"As a precaution, the cylinders were cooled down as some can explode when exposed to heat," a statement on the brigade's website reads.
"Fire crews from Soho and surrounding fire stations were at the scene."
Earlier in the statement, the brigade said: "Part of the basement, ground, first and second floors of the building under refurbishment were badly damaged by the fire".
The cause of the fire is under investigation and road closures are in place.
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