The WAAF was the female auxiliary of the Royal Air Force, and at its peak numbers exceeded 180,000, with over 2,000 women enlisting per week. These women were incredible because they were not allowed to be aircrew and never experienced active combat, but still faced the same level of danger as the male fighter pilots in the RAF. They, like Maddie and Julie, worked mostly with wireless communication, codes, and undercover intelligence operations. They were very much the backbone and support of the British airforce, and were paid two-thirds of what the men in the RAF were paid.
The ATA was the only organization in which women were allowed to fly planes, so naturally it is the group that Maddie wants to join (and eventually does). They transported new, repaired, and damaged military aircraft between assembly plants, factories, scrap yards, and airfields. This work was also a little more dangerous than the usual as it involved piloting of damaged aircraft.
The SOE, or Special Operations Executive, was so secretive that at the time hardly anyone even knew it existed. They were a British organization formed to conduct espionage, sabotage, and reconnaissance in Axis occupied countries in Europe, and to aid local resistance movements (such as Julie's assignment in Ormaie and how she was supposed to help the French Resistance before she was captured). The SOE was also known as (by the few who knew of it) the "Baker Street Irregulars", "Churchill's Secret Army", or, my favorite, the "Ministry of Ungentlemanly Warfare". They worked a lot with the auxiliary organizations of the British military, which is most likely how Maddie and Julie manage to cross paths again. The SOE worked a lot with radios/code, and the main weapons they used were bombs planted in sabotage missions (the bridge battle scene at the end of the novel). SOE operations were actually mounted in France to assist the resistance movement, and a couple of women were on the teams, so Julie's tale of espionage and interrogation in Ormaie isn't actually as far-fetched as it may seem.