The store group - which posted flat annual pre-tax profits of£39 million at the start of the month, and like-for-like sales down 1.8 per cent - said that Liggett had resigned and would work his six-month notice period until April.
A spokeswoman said that the process to find a replacement had begun and denied that Liggett's departure had anything to do with tough trading conditions.
She added: 'Andrew wants to spend more time with his family. He has been with the company for 11 years and we all wish him well for the future.'
Liggett will remain in his post for Topps Tiles' annual results on November 28.