It makes sense for TV channels to broadcast with their schedules divided into half-hour chunks, so that (including ads where applicable) 30, 60 and 90-minute episodes are typical. The half-hour comedy format has been prevalent in UK and US TV since at least the 1950s (e.g. Hancock's Half Hour and I Love Lucy), and animations in Japan, the UK and the US have long also had a half-hour format.
I think the hour-long drama format is a more recent standard, since for example The Quatermass Experiment and Dragnet both used a half-hour format in the 1950s, but again it applies to both the UK and US. Though usually child-friendly, Doctor Who is clearly intended as a drama, and experimented with an episode-doubling format in 1985, only to then abandon it until 2005, when it stuck. Whether this is because a tolerance for longer dramas became locked in c. 1990 I don't know.
How and when did these conventions develop? How independent were nations' paths with this? In particular, how far did the US influence the UK and Japan?