The fire broke out at Crawley Hospital in West Green Drive, Crawley at 13.36 pm.
It's believed to be in a sixth floor store room. There are no reports of casualities.
50 firefighters are involved with tackling the blaze.
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Their warning depends on whether negotiations for a post-Brexit Britain do not offer freedom of movement for people, capital and goods.
Wednesday morning's weather for the east of the region
Wednesday morning's weather for the west of the region