Breakfast radio programming was actually started in September 1939 when World War 2 commenced, and the BBC ended their National and Regional programmes, which until then would only start their broadcasting day at 10.15am.
This fact always astounds me. France, for instance, had quite a few stations with morning programming in the 1930s -- but then again, France had commercial broadcasting before WWII. (It was abolished after the war).
One would think that mornings would be a high-priority time slot for a radio station even back then. But RTE in Ireland was even worse -- they didn't have morning radio in the 1960s (!), a time when car-based listening was already widespread.
Public broadcasting is truly a godsend, but its failure to provide a round-the-clock service, both in radio and television, for so many years is difficult to justify, especially in countries where it enjoyed a monopoly. After all, it's often said that dead air is a cardinal sin in broadcasting.