Another one that literally gave me nightmares at the time was "QED: A Guide to Armageddon":

https://www.youtube.com/watch?v=9GJttnC8PoA

You almost got the idea that the BBC didn't approve of nuclear warfare.

NB A thing worth noting about Threads is that is based on a nuclear attack scenario that is regarded as rather optimistic - a real Soviet attack would probably have been much worse:

https://en.wikipedia.org/wiki/Square_Leg

Threads is outstanding. I rarely if ever had a nightmare after watching something but that movie is so frightening and depressing that the first time I watched it I could barely force myself out of bed the next day. Incredible work by the BBC.

Same with me. I was seventeen in 1984 when it was first shown but didn't see it at the time. I finally watched it a few years ago and had a night of unusually disturbed sleep followed by two days that were mentally tinged with vague feelings of doom and contamination. Not something I'd want to experience again.

In the same vein: The War Game.

Recorded in 1965, but not shown until 1985 as

"the effect of the film has been judged by the BBC to be too horrifying for the medium of broadcasting. It will, however, be shown to invited audiences..."

https://en.wikipedia.org/wiki/The_War_Game

The quite I remember from The War Game is:

"the sound of the blast from a thermonuclear bomb has been likened to that of an enormous door slamming in the depths of hell."

I was born after the Berlin wall came down, so I got to miss all the fun of living under constant threat of looming nuclear annihilation, but Threads still had a profound effect on me when I watched it. It may be dated now, sure, but it still hits with a hell of a force.