More than 30 firefighters helped to tackle the blaze on Great Eastern Street in Shoreditch from 03:45 BST.
LFB has since apologised after its joke about the fire was met with a mixed response on social media.
It said: "Sorry if we caused any offence by using the term hipsters."
LFB added: "Hope #Shoreditch businesses are back on their feet soon."
An investigation into the cause of the blaze is due to begin.
The apology came after criticism of the joke on social media. Mike O'Brien tweeted "enough with the hipster jokes. People's livelihoods have been ruined".
Others were more amused with Twitter user Debbie commending the brigade for a "great job", saying the hipster comment "made me spit my tea out".
However, Pete Carrier tweeted to say "are you worried that Met Police Helecopter [sic] are getting all the attention?"
His comment made reference to a situation earlier this week when the National Police Air Support Unit in London came under criticism for zooming in and taking a photograph of comedian Michael McIntyre before posting it on its Twitter account.
A building housing a pop-up restaurant in east London has been partially destroyed by fire, but "fortunately no hipsters were injured", London Fire Brigade (LFB) has said.