Is there a name for this design style - use of flat colours for dimension and shading - that was so prevalent in UK travel posters of the 1930s?
I think your best chance for any sort of official title would be simply, Travel Posters or Golden Age of of Travel Posters (or .. Travel Art).
It is a blending of a number of styles especially Art Deco, Futurism, Swiss Style and Art Nouveau. The one you show might be a newer poster / postcard trying to imitate the style as its a bit more complex and smooth than most would have been in that era due to technological limitations. On its own however it doesn't have a style that I'm aware of or was able to find.
It is also largely associated with a period known as The Jet Age which doesn't really have a style so much as its when mass tourism took off by way of flights. While it doesn't have its own sort of style there are many things that became intertwined between it and the aforementioned styles such as automobiles, fashion, and really industrial design as a whole. Jets and travel were the in-vogue thing. Everything wanted to be a part of it. I bet if one were to really research and dig into the subject you'd find that many of the post-styles came as a direct result of the Jet Age.
And if there is one single entity that captures the mind and spirit of that era its is TWA Flight Center by Eero Saarinen. It is an absolute crime that its being turned into a hotel instead instead of Cultural Heritage Site. It is at least protected on the National Register of Historic Places so the exterior will be largely in tact.
If you’ve visited JFK Airport in New York City, you’ve probably seen the Trans World Airlines (TWA) Terminal. Built in 1962, the shapely building was designed by Eero Saarinen to usher in the Jet Age.
And of course the famous: