Prior to 1938 (and throughout much of that year) there were very few
regular programmes broadcast on BBC radio. Programmes were generally put together as 'one offs', with no fixed pattern to the broadcasting. One of the few regular programmes which was broadcast (and which would have attracted very large audiences on Saturday evenings during 1938) was 'In Town Tonight':
http://en.wikipedia.org/wiki/In_Town_Tonight
The first regular comedy show, to be broadcast by the BBC, first went on air in 1938, to massive acclaim. It was Band Waggon:
http://en.wikipedia.org/wiki/Band_Waggon
Chris