Threads (1984) – Documentary style account of a nuclear holocaust and its effect
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My gf and I couldn't stop thinking about it for like a month - and looking back on it, I think I was walking around a little bit depressed. Too real.
I don't know if there's much to gain from watching it. 5/5 bags of popcorn.
For some reason I also still remember a scene from https://en.wikipedia.org/wiki/Special_Bulletin - the news crew trying to understand why the NEST bomb squad was running away just before cutting out...
I thought the scene in The Day After where the silos open and the missiles go up was the most chilling thing to experience. At that point you've got a couple of minutes until the end of the world ...
This movie has one.
There's also a similar but more famous American film: https://en.wikipedia.org/wiki/The_Day_After
It's pretty similar to the one you describe. It centers on Lawrence, Kansas, which doesn't get nuked, but has to deal with fallout, refugees, insufficient resources, etc.
Great book, great movie.