The Wiltshire-based company suspended trading on the Stock Exchange in November, following a cash crisis caused by production problems. Share prices crashed when trading resumed in December following a profits warning.
The Halls, the founders of the company, said now was an "opportune time to move on to other challenges", with the integration of ice cream brands Loseley Dairy Ice Cream and Granelli now complete, and improvements at its Cwmbran site progressing.
They will remain holders of 20,492,800 ordinary shares in the company - 5.9% of its share capital.
The Halls have also expressed their support for the proposed appointment of William Mapstone as executive chairman - subject to shareholder approval at the EGM convened for 31 January.