Well that's my recollection from when I was a nipper but this suggests it was more complex than that with different serials being shown on a fre channels at various times.

My main memory is of getting up early to watch the B&W serials on ITV before the proper telly started but it may be I have conflated things into that memory. I definitely wouldn't have thought they were on BBC 2 at teatime as I recall things like Star Trek TOS being on at 6 and there being a battle to see if we'd watch that or the news. However, the movie serials were presumably cheap filler so different channels presumably filled up time with them at various points.

I will do more digging.