New Kent Road was closed to traffic on Monday night while firefighters tackled a blaze on the top floor of St Matthew's Court.
The London Fire Brigade sent six fire engines, a turntable ladder and two command units to the scene.
Crews and vehicles were dispatched from fire stations in Old Kent Road, Dowgate, Soho, Whitechapel, Peckham, Islington and Lewisham.
St Matthew's Court is a four-storey block of flats built in the 1990s on the site of the old St Matthew's Church.
The block is owned by the Southwark & London Diocesan Housing Association, which is currently in the process of being taken over by AmicusHorizon.
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