This video is from 1956 shows the process of making an LP from vinyl.
https://www.youtube.com/watch?v=xvYXkRIz9OE
But I do know in 1958 they were still making some pop 78s from a breakable material, so I'm assuming shellac.
It was pretty much unavailable during the war years as it was used in the manufacture of electric motors.
I remember Humphrey Lyttleton mentioning in an interview about fifteen years ago, that during the wardue to the scarcity of the material, to obtain a new record he had to "hand one in."
I'm also aware that to make what shellac there was go further, some records produced had an inner core of sawdust.