More than 80 firefighters are currently tackling the blaze at the five-storey building just around the corner from the famous glass landmark.
London Fire Brigade (LFB) confirmed 12 fire engines had been dispatched to the scene in Great Guildford Street shortly before 4pm.
And dramatic video shows the emergency services descending on the street as smoke billows from the roof of the building.
The fire had broken out inside a third floor flat, an LFB spokesman said.
The cause of the fire is not known at this stage.
More to follow…