I agree, even taking into consideration that they royals used to be extremely traditional, if not to say old-fashioned esp. Queen Mary, the fashion is def. not pre-WWII but much earlier. Plus in 1935 the princess royal would have been pushing 40 and there is no way the woman in the photo is that old. Back in those days, 38 was considered really "mature" and a woman would not wear this kind of dress.
And last but not least: the shoes!
The shoes are one of many pointers! And there's a difference between being a season or two behind the times, and being dressed in the tip-top of fashion from two decades previously, hair included.
Queen Mary was a bit of an exception (I believe I've read that George V really liked her in the older styles, so she kept them on??) but that was also not until she was really even past middle age. Many older women did not adopt the new extremes of fashion in the late 1920s.