Within days of coming to power, Gordon Brown had to make a decision with potentially massive consequences for Britain and the world.
Would he, in the event of a surprise nuclear attack in which he was killed before he could react, want Britain's last line of defence - a lone Trident submarine on patrol somewhere under the Atlantic - to retaliate?
Brown wrote his answer to that question four times, in long-hand, in the form of letters addressed to the Royal Navy submarine commanders who, we must all hope, will never be required to read one of them.
The letters are sealed in a safe aboard each of Britain's four Trident submarines.
If Britain is substantially destroyed by a nuclear strike and the prime minister is killed, the captain of the submarine on patrol (one is always out there, armed and ready to strike) will open his safe, take out the prime minister's instructions, and act on them.
For a BBC Radio 4 documentary, The Human Button, we were given unprecedented access to Britain's nuclear weapons infrastructure.
If I had lived after having pressed that button, I would never, never have forgiven myself
We have seen how the system works, visited the secret command bunker upon which it relies and watched a firing exercise onboard HMS Vanguard, the submarine which is - right now - out there somewhere on patrol.
But the biggest question is, of course, the hardest to answer. Would Britain ever, in any circumstances, actually unleash its nuclear arsenal?
We are unlikely ever to know what Gordon Brown has decided. His so-called 'Last Resort Letters' will be destroyed unread when the premiership changes.
And only two decision-takers have ever revealed what they would have done in the almost unimaginable scenario of a bolt-from-the-blue attack.
Jim Callaghan, speaking to Peter Hennessy for a BBC documentary in 1988, said that "if we had got to that point where it was, I felt, necessary to do it - then I would have done it".
"I've had terrible doubts of course about this. And I say to you that if I had lived after having pressed that button, I would never, never have forgiven myself."
I would find it very, very difficult indeed to agree to use a nuclear weapon
Now Lord Healey, too, has revealed what he would have done. As defence secretary in the 1960s, Healey was asked by Harold Wilson to be an 'alternate decision-taker'.
In a period of rapidly-escalating international tension, Healey would have been required to go to the Royal Air Force's Bomber Command bunker. (In those days the primary deterrent was carried not on Royal Navy submarines but by RAF V-Bombers - the Victors, Valiants and Vulcans.)
There he would have stood alongside the head of Bomber Command, ready to take the retaliation decision if Wilson was killed before he could take it himself.
"I did feel rather worried about it because I knew it would be a very difficult decision to take," he says.
"I realised I would find it very, very difficult indeed to agree to use a nuclear weapon - and I think most people would."
What if the head of Bomber Command had turned to him, as Soviet nuclear weapons were already raining down on targets across the United Kingdom, and implored him to retaliate? Britain is being obliterated forever, he might have said, at no cost to the enemy.
Healey is clear. "I think I would still have said that that, I'm afraid, is no reason for doing something like that.
"Because most of the people you kill would be innocent civilians."
Healey's admission is remarkable. At that time, in the very darkest days of the high Cold War, the threat of nuclear conflict sometimes felt close.
Today it does not. Yet the possibility remains. And as long as Britain retains its nuclear deterrent (and in 2006 the government decided that it would do so), someone, one day, might yet have to make that terrible decision for real.
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