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.

Made from glass-reinforced plastic, 60 life-sized ewes have formed an art trail in unexpected places between Keswick and Windermere.
Each sculpture is sponsored by a local business and decorated by an artist.
The Lake District Calvert Trust said locals and tourists had been sharing photos of the "beautiful ladies" via social media every day.
The Go Herdwick project is part of the trust's 40th anniversary to raise funds for a new facility at its Old Windebrowe site.
The 60 ewes, inspired by London and Bristol's Shaun the Sheep figures, will be joined by 50 lambs to coincide with the reopening of the A591 in May.
The trust's business manager, Justin Farnan, said: "The closure of the A591 could have been seen as a setback for us, but it will be open for the majority of the trail.
"We are very pleased that Go Herdwick will be able to help drive tourist footfall to places such as Grasmere, both before and after the road is reopened, and that we can give something back to the wider community in what has been a difficult time for many businesses and residents."
The Herdwicks will be rounded up and auctioned for the trust in October.
The charity, which provides outdoor holidays for people with disabilities, will use the money to develop the Grade II-listed building at Old Windebrowe into a rehabilitation centre for people recovering from strokes and for those with brain injuries.
Herdwick sheep are native to the Lake District and often graze at heights of about 3,000ft (915m).
Recognised as one of the hardiest British sheep breeds, in 2013 it was awarded protected status by the European Commission.

The Competition and Markets Authority (CMA) said it had identified 33 local areas where pubs would not face sufficient competition after the deal.
Heineken, which already owns 1,100 pubs, must submit plans to the CMA by 20 June or face an in-depth inquiry.
However, the brewing giant said it would address the CMA's concerns.
"This decision by the CMA acknowledges that there are only a small number of local areas where competition may be diminished due to our acquisition of the pubs," said David Forde, managing director for Heineken UK.
"We are confident we can offer the CMA suitable undertakings to satisfy their concerns."
The preliminary CMA investigation concluded that the deal would not damage the chances of Heineken's competitors selling their own products, as the pubs being bought only make up 4% of the market.
It also felt that it was unlikely Heineken would reduce the choice of beer and cider available in the Punch pubs, as this could lead it to lose business.
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.
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A flock of decorated model sheep has invaded the Lake District in a bid to raise £1.3m for charity.
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Heineken has been told to address fears that its purchase of around 1,900 pubs from Punch Taverns could affect competition in some areas.