Two directors of Anthony Kid Agencies, John Burnham and Steve Greenman, resigned this week.
Both were both board members at AKA when Cox acquired it for £14m in July 1998.
The former chairman's son, Simon Kent, has also left.
Neil Utley, chief executive of Cox's retail division said: "It is always disappointing to lose people, but life moves on and we will continue to go from strength to strength."
Utley refused to say where the two directors have gone, although there has been market speculation that they may seek to form a new underwriting operation at Lloyd's.
Utley added that AKA has a very "fluid board", with all directors having wide-ranging responsibilities. Both men looked after accounts and sales, while Burnham's speciality is IT.
Burnham has now left the company, while Greenman is working out his leave. Their departure means that only chairman Robert Ayrton is left on the board since the Cox took over AKA.
