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The London Fire Brigade (LFB) was called to the blaze in Harvey Street at 3.20pm, and the fire was under control by 4.18pm.
Part of a fourth floor flat was damaged by fire on Tuesday.
Four fire engines and 21 firefighters and officers attended the scene from Kingsland, Shoreditch, and Islington fire stations.
Harvey Street is situated less than 1,000m from Kingsland Fire Station which is one of 12 stations across the capital earmarked for closure under plans by the LFB to save £28.2million over the next two years.
No one was injured.
The cause of the fire is under investigation.
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