Churchill Square has been evacuated.
Four fire engines are now at the scene, two from Preston Circus and two from Hove, along with the Incident Command Unit from Lewes.
An acetylene cylinder had caught alight in a storage area where some building work was being carried out.
The fire is now out and crews are cooling the acetylene cylinder using one hose reel jet. The cooling process is expected to take some time.
Churchill Square Shopping Centre will be closed for at least four hours.
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A dull and damp start but it will become drier and brighter from the north this afternoon but stay cold and windy.
A damp and cold night ahead. Valentine's Day will start cloudy but become brighter in the afternoon. Risk of showers along the Kent coast.
Cold and damp tonight with outbreaks of rain. A cold and dull start to Valentine's Day but becoming drier and brighter by the afternoon.