By the 1930s, there were time signals broadcast by radio. I can't speak to Europe, but in Canada, radio time signals were started by the Meteorological Service of Canada, then taken over by astronomers at the Dominion Observatory, before moving to its current custodians at the National Research Council in the 1970s. The Canadian Broadcasting Corporation started a once-daily broadcast of the time signal for 1 pm Eastern Time (GMT/UTC-5, or GMT/UTC-4 for daylight time) in 1939 that continues to this day. I know I would regularly set my wind-up watches to that signal when I was a kid. (There are also continuous time signals broadcast on station CHU at different frequencies, which began in 1923, similar to the US broadcasts on WWV, WWVH, and WWVB.)

Sources: "1939: The beginning of the long dash…", CBC radio broadcast from Feb. 4, 1974. Announcer: Alan Maitland

"NRC short wave station broadcasts (CHU)", at the website of the National Research Council.