When WWII breaks out, an elite force of German U-Boat commanders, under the direct command of Vice-Admiral Karl Dönitz, attempt to starve Britain into submission by sinking hundreds of thousands of tonnes of their merchant shipping in the mid-Atlantic. Vera Laughton Mathews heads the newly reformed WRENS, and recruits bright, astute, and mathematically minded women into the service. Meanwhile retired naval commander Gilbert Roberts, who has been out of the service, is keen to return to his career and use wargaming to sink the U-Boats.

When Gilbert Roberts arrives to set up his proposed Western Approaches Tactical Unit (WATU) for U-Boat wargaming, he receives a decidedly frosty reception from Admiral Sir Percy Noble who is convinced the Allies already possess the tactics and expertise to defeat the Kriegsmarine. Nevertheless, Roberts presses on and, enlisting the help of Jean Laidlaw and a small team of WRENS, based in Liverpool, begins the process of round-the-clock wargaming to devise tactics to outmanoeuvre the U-Boat attack formations.