A 200-metre exclusion zone has been set up to protect residents from the possibility of exploding gas cylinders, a London fire brigade spokesman said.
"A number of gas cylinders including one acetylene are involved in the blaze," the representative said.
"The brigade was called at 00:29 BST and around 50 firefighters and ten fire appliances are currently at the incident."
No injuries have been reported.
Lewisham council said the evacuated residents had been taken to Deptford Park primary school, where refreshments and bedding were provided
That school and the nearby Sir Francis Drake primary school in Scawen Road have both been closed to pupils.
Commuters have also experienced major disruption on all rail services coming in and out of London Bridge, Cannon Street, Waterloo East and Charing Cross in the south of the capital.
"Any diverted trains will go into Victoria or Blackfriars and tickets can be used on London buses, the underground and Docklands Light Railway," a council spokesperson said.
A statement on the website for Southeastern Railway detailed a number of routes which will be diverted as a result of the fire as well as two - Ramsgate / Broadstairs to Cannon Street and Tunbridge Wells to Charing Cross and Cannon Street – which will not run.
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