Whitworth, who has been executive chairman since 2001, said someone else should chair the company through its next phase of development.
Sprue Aegis has shed two-thirds of its value following a dispute with one of its main distributors and a profit warning last month.
Whitworth will stay on the board as a non-exec, but Sprue will appoint a new non-exec chairman.
The fire alarm products group has also appointed Mike Stilwell as group finance director.
He will take up the job from December 3 after he has worked his notice period at his current employer, Synectics PLC, where he is finance director.