Musician David McAlmont was among a crowd of people gathered at the cordon's edge.
He said: "I saw the smoke from St Martin's Lane and followed it all the way here. It was only then that I realised what was happening.
"I'm supposed to be playing a gig tonight at the Pizza Express in Dean Street so I don't know how this will affect it."
It was the second blaze to hit Soho in as many days. On Thursday, fire crews were called to a building in Newport Place which housed a restaurant and offices.
The fire damaged the basement of the five-storey building but no-one was hurt.
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