Wikipedia attribution link for picture of Hut 4 at Bletchley Park:
I watched the BBC film "Code Breakers" with link above (59 min), directed by Julie Carrie, so it doesn't seem to be the same film. It starts with the accomplishment of Turing in breaking Enigma and goes on to present the work of William Tutte and Tommy Flowers in breaking the German Lorentz machine. The mathematics of code breaking rather resembles group theory and vector spaces (maybe rings, too). Flowers designed the electrical components of the most advanced computer at the time, and on D-Day his staff had to work in a wet environment to keep it from shorting out. Computer work was very much more physically demanding then, but the military really did use "mathematicians" (which was my MOS in the Army 1968-1970).
Errata (apologies): The word "Turning" in the URL name should be "Turing", corrected manually. Automated typing is too easy, and word processor spell-checks don't catch this.