The wide acceptance of wrist watches by military personnel started during the trench warfare battles of WW 1. The early “wristlets” were originally seen as items worn by women only, yet their usefulness was shown before they were fully accepted by the British Army Officers involved in general procurement. The issuing authorities still considered the pocket watch to be more robust in extreme conditions.
By 1917 the War Department took a bold step forward and obtained samples of wrist watches for field testing. Even by WW2 the humble pocket watch was still seen as a more useful and reliable item
During WW2 the British Army were issued with a type of watch called an ATP (Army Trade Pattern). It was manufactured by 17 different Swiss suppliers. They mostly conformed to a standard pattern of 15 jewel movements, mostly silver/white dials with luminous hands. To confirm military issue the letters ATP were placed on the caseback. These watches were then replaced with the WWW watches that began to reach Army service personnel by 1945. These being supplied by Buren, Vertex, Timor, Record, Omega, Lemania, Longines, IWC, Grana, Eterna, Cyma and Jaeger LeCoultre.
The use of wristwatches by RAF pilots became very widespread as accurate timings were required to assist in navigation. More often than not it was just the pilot and navigator that were issued a timepiece.
It was even harder for Naval personnel to be issued with a wristwatch, it was mostly limited to the small numbers of Fleet Air Arm Pilots & Navigators. Although the Navy did have a number of very expensive as well as accurate chronometer watches on board the fleet vessels.
WW2 RAF Pilot / Navigator Omega 6B/159 watch
German 30's Zenith Luftwaffe