OK, so this one I'm not conpletely sure about. Extrapolating from other Websites, I gather that this song has two titles, and that it's the song referred to above as "First Things First," written by Alex Comfort.

70. Ban Ban Ban the Bloody H-bomb (to the tune of John Brown's Body)

BAN BAN BAN THE BLOODY H-BOMB
[FIRST THINGS FIRST]
(allegedly by Alex Comfort)
(tune: John Brown's Body)

To hell with all the humbug and to hell with all the lies
To hell with all the strontium continuing to rise
To hell with all the Charlies with a gift for compromise
If they won't ban the H-bomb now

[Chorus]
Ban ban ban the bloody H-bomb
Ban ban ban the bloody H-bomb
Ban ban ban the bloody H-bomb
If you want to stay alive next week

Macmillan and the Tories are out to wait and see
They think the great deterrent will secure the victory
I don't know if they scare the reds, by god they frighten me
If they won't ban the H-bomb now
[Chorus]

Gaitskill's labour party are preparing for a sell
They want to get the votes and keep the atom bomb as well
But strontium will send us all to shovel coal in hell
If we don't ban the H-bomb now
[Chorus]

Now half of them are barmy and half of them are blind
They've all been talking far too long, its time they all resigned
And the way to shift a donkey is to wallop its behind
So we're going to ban the H-bomb now
[Chorus]

We're going to stop the loonies and preserve the human race
We're going to save our country ‘cause we love the dear old place
We might have to stuff a rocket up the rocket builder's base
But we're going to ban the H-bomb now
[Chorus]

Somewhere in the States they've got a button painted red
If anybody sits on it we'll all of us be dead
Meanwhile a million children are waiting to be fed
So we're going to ban the H-bomb now
[Chorus]

Source: Socialist Songbook, http://wolvestuc.org.uk/index.php/links/socialist-songbook?showall=&start=5

"Ban, Ban, Ban the Bloody H-Bomb" by Alex Comfort, is supposed to be in Tom Glazer's Songs of Peace, Freedom, and Protest (1971), pages 16-18

I thought I had that book, but I can't find it. There's a Joe Glazer book with a similar title, and I keep getting the two mixed up.