Farr - formerly BBC director of public service marketing - quit after two years heading the agency's UK and European business.
Deputy MD Barry Leggetter takes over as UK MD, but said he will not inherit the European aspect of Farr's role.
GHI chief executive Rich Jernstedt said: 'At the time we appointed Sue, we hoped we would be in a position to proceed with an aggressive European acquisitions strategy.
'We need to refocus on the core UK market until the economic climate allows us to return to our acquisitions initiative,' he added.
Farr has not announced her next career move, but sources suggest she will return to the marketing services sector.
Leggetter, who previously headed Countrywide Porter Novelli London as joint managing director, said his immediate priority at GHI is to continue growing the public affairs practice.