The earliest citation I could find uses the longer (and clearer) phrase
fresh food desert:

The healthy-eating boom that swept muesli-belt Middle England through the 1980s by-passed Tipton. Money was too tight. Like thousands of other communities across Britain, it had been transformed by the exodus of the big supermarkets to out-of-town greenfield sites into what the experts call a 'fresh food desert'.
Judy Jones, "The fast food trap," The Observer, January 21, 1996
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