A spokeswoman said there were no immediate plans to replace him. Group chief executive Jean-Noel Labroue will take over Fox's largely supervisory role.
Labroue said: 'I would like to thank Simon for his contribution to the transformation of Comet and wish him every success for the future.'
Fox joined Comet in 1998. He was previously a senior consultant with the Boston Consulting Group and founder and managing director of Office World.