Williams has been with Thresher for three years. He has agreed to remain in place until his replacement is found.
He joined from the Diageo subsidiary Burger King Europe, where as president he reversed its fortunes.
He has accomplished a similar turnaround at Thresher
which went from operating loss of £28.6m in 2000 to operating profit of £15.8m last year.
Williams said: “The company is unrecognisable from the one we found three years ago and now is the time is right for me to move on to another challenge.”
Terra Firma, the venture capital company that bought Thresher Group three years ago, denied press speculation that Williams’ departure signalled its intention to sell off the business.