Britvic said the split was due to HHCL's new parent Red Cell working for rival Coca-Cola. Red Cell handles the US ad account for Coke Classic through its New York agency, Berlin Cameron/Red Cell.
Red Cell, WPP's fourth agency network, bought a controlling interest in HHCL & Partners for £4m in January.
"Given that the acquisition by Red Cell has resulted in a conflict of interest within the agency, the time is right to look for a fresh approach," said Andrew Marsden, Britvic category director.
HHCL/Red Cell will complete a number of campaigns already planned for the summer, Robinsons' peak sales season. However, Britvic is keen to hire an agency by July and will hold pitches shortly.
Robinsons is the UK's second-biggest soft drink brand. In 2002, it grew annual take-home sales by 14% to £232m, according to AC Nielsen.
Lee Daley, HHCL/Red Cell's chairman, described it as "a sad day for the agency".