I can't think of another one bleaker than Threads.
The other three Barry Hines films that I've seen have all been bleak. Kes and The Price of Coal have some humour in them, but the endings make you feel almost sick in both. Looks and Smiles is bleak throughout with little humour, but doesn't have any particularly shocking bits.

Quiet Earth is a great movie!
Here's the trailer:
"I'm a vehemently anti-nuclear, paranoid mess, harbouring a strange obsession with radioactive sheep."

quiet earth
http://www.imdb.com/board/10089869/?ref_=nv_sr_1

"When the Wind Blows", perhaps. Also about Nuclear War aftermath IIRC.

Here's your man:
The War Game (1965)

The Road and The Grey Zone are both quite bleak.

Hercules in new York
you must do what you think I right of coarse

Must be a Jewseriously who else could equate what happened in the second world war to the end of the world?

On the beach the new version. when the young Australian couple with their toddler decide rather than face death by radiation they will take their own lives with the government issued drug suicide kits.then the wife begs her husband at the end they have just one more day.very heavy scene!

Combat Shock

Not a nuclear film but Johnny Got His gun is a pretty damn grim movie

What about When The Wind Blows, The Road, and though not dealing with Nuclear holocaust Requiem for a dream is pretty bleak.

I second these. Dead Man's Letters is the best nuclear apocalypse film i've seen and Come and See is one of the best war films i've seen as well. Two of my favourites.
"Having a heart is heartbreaking."

Dead Man's Letters
and
Come And See
.

I'm surprised no-one mentioned Come + See. a tale of a boy who's village is destroyed by the nazis

Even if you hate Uwe Boll, give Postal a try, be offended or entertained.

"Fail Safe" scared the beep out of me. I saw it in my college class and that ending.

In terms of the final outcome and all its repercussions, then "Fail Safe" would be (and, of course, covers the same ground) but "Threads" shows this in detail and, as such, is bleaker on a one-to-one level.

The War Game, made by the BBC in 1965 was deemed by the directors to be too bleak to air and so didn't get shown on TV until 1985. It shows the real effects of nuclear war and is much bleaker than Threads and also has very disturbing imagery such as a young boy who's eyes are melted by the flash.
Bearing in mind that bombs are much more destructive now 50 years later it makes you think that if there was a war now there really probably wouldn't be any survivors at all after a few years.

letters from a Deadman for sure
"I'm a vehemently anti-nuclear, paranoid mess, harbouring a strange obsession with radioactive sheep."

Like one of the earlier posters I was thinking about Letters from a Dead Man as a likely candidate. The thing that stands out to me in that movie is how utterly filthy everything is presented: Absolutely nothing is left but a radioactive wasteland of ruined concrete bunkers, rust, decay, sickness, orphans, suicides and depression. And it all takes place in a sickly yellowish atmosphere no-one survives in without massive protection. The world (and mankind with it) seems to be utterly doomed.
Threads have much of the same bleak outlook, but while it seemed like the UK was going to hell I never really got the impression the entire world was in the same situation. In LFADM the protagonist openly speculate that the human race faces extinction.
On the other hand, one of the strongest aspects of Threads is to show how society collapse, while in LFADM everything is in chaos from the beginning.

No, this one is the grimmest i have ever watched.

I watched that in connection with my IR degree at St Andrews. I agree it is depressing, but Threads pips it for me because the thing about 'Fireflies' is that we know that, however badly the characters suffered, there's a world out there of people who got on with their lives, and ultimately Japan will recover and thrive. With Threads, the scenarios the characters are experiencing are being played out, as far as we can tell, all over the world, and all humanity is bound for oblivion.

Another to add to the list of bleakest films: Studio Ghibli's Grave of the Fireflies - the film follows a brother and sister during WW2 in Japan. If anyone has seen this film on this board, I think we can agree that it is depressing.

"Testament" with Jane Alexander and William Davane. It came out about the same time as "Threads". Made me want to slit my wrists.