Hunton, 45, will not be replaced. He and Walsh are in negotiations about the details of his exit.
During his time at the agency, Hunton is credited with leading successful pitches for the £9 million Twinings account and the £13 million John Lewis account. However, according to sources, he applied for the chief executive post, but was overlooked by Steve Gatfield, the Lowe Worldwide chief executive.
Hunton joined the agency in 2005 after a spell at Quiet Storm. He was hired by Walsh's predecessor, Garry Lace, who left in May following an investigation into his dealings with Sir Frank Lowe.
Hunton is the former chief executive of McCann Erickson London. He left in 2004 after five years, during which time he was credited with building strong relationships with MasterCard and Bacardi.