A Coke statement said: "We had different perspectives on the creative and strategic direction of some brand activity; we have decided to part company."
Coke declined to comment on future PR plans for the brands.
JCPR has also been hit by the resignations of two board directors: Clare McKeown will leave this month after seven years; nine-year stalwart Ian Withington has already departed.
Jackie Cooper was first hired by Coca-Cola in 1997 to handle a secret consumer push for Fanta. It was took on PR for Coke's tropical carbonate Lilt.
To take on Coke the agency resigned contracts with drink brands Red Bull and Snapple, worth a total of £175,000 in fees.
It was later appointed to work on the launch of Coke's Alive carbonated fruit drink.
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