This is an even less well documented aspect of the GWR’s activities than the ships! I shall need some help documenting links and sources of information!
The GWR formed its own air service in 1933 but operated independently for only a year before the Railway Air Service was formed by the Big Four railway companies in collaboration with Imperial Airways to provide internal services to connect with Imperial’s international flights – the modern equivalent ofd FlyBe and Easyjet, in many ways. One of the most important routes was Cardiff to Plymouth and Cardiff to Liverpool and Birmingham. The RAS was absorbed into the nationalised company BEA in 1947
There is a discussion here, with some nice posters and quite a detailed account of the Plymouth based GWR air services here.