He was made managing director in 2005 following roles as facilities and communications director.
Barmer has left to go travelling.
Robin Shenfield and Pat Joseph will remain as chief executive and chief creative officer and although many of Barmer's responsibilities have been redistributed, the company may employ an operations director to take on some of Barmer's responsibilities at some time in the future.
The Mill is a visual effects company with facilities in London and New York. Its work covers commercials, television, film and more.