Why, in the second year of the war against Germany, did Hess believe that he would be welcome in Britain?
Why did he think Britain would jump at his plan for an immediate ceasefire and then a joint British-German attack on the Soviet Union?
What role did the British Secret Intelligence Service (SIS) play?
Why did President Roosevelt say, when briefed by Churchill on the Hess affair, "I wonder what is really behind this story?"
And, above all, why more than 50 years after the war are the Foreign Office files on Hess still closed and due to remain so until 2017?
Using a length of electrical extension cord, Rudolf Hess, a frail 93, hanged himself in the garden of Spandau Prison, Berlin, on 17 August 1987; or did he? Like so much of his life, Hess's death remains a puzzle. Why should a man who had survived 40 years in an Allied-controlled prison commit suicide when an international campaign for his release looked like succeeding?
A senior Scotland Yard detective, Howard Jones, thought there was sufficient evidence to suggest Hess had been murdered, and submitted a report to the Director of Public Prosecutions saying so. But, not surprisingly, the DPP did not agree and nothing happened.
There was certainly a motive for Hess's murder. Once free he might have spoken out and told the real story of why he crash-landed his Mess-erschmitt in a field near Glasgow. And what a story it would have been.
We know some of it. Hess was on a peace mission. With or without Hitler's blessing - there is no agreement on this - he planned to meet with British leaders, persuade them that it was madness for Britain and Germany to continue to fight each other and convince them that they should unite against the Soviet Union. How different history would have been if Hess had succeeded.
But why would Hess imagine that anyone in Britain would listen to him? The most recent book on Hess, by the German historian Rainer Schmidt, claims that the whole Hess affair was a devilishly cunning plot by the SIS to lure Hess to Britain with forged correspondence purporting to come from a British group which would support his peace initiative.
If the correspondence was faked and the only aim was to lure Hess to Britain, what was the purpose? What use would he be to us as a prisoner? The only possible reason would be to pull off the propaganda coup of the war. We can imagine the headlines, "Nazi Leader Defects to Britain. Says Hitler Barmy".
This is certainly what the German leaders thought would happen. In anticipation of it, Goebbels, the German propaganda expert, quickly mustered a defence: "The matter has to be treated as the act of a madman. How else can it be explained, above all to our Axis friends who will otherwise begin to have doubts about the solidarity of the alliance?"
Six days after Hess's arrival, with the British government remaining silent, Goebbels was delighted. "It apparently hasn't occurred to London to do the obvious thing and make statements in Hess's name without reference to Hess himself. It seems we have a guardian angel."
So if the SIS had not lured Hess to Britain to pull off a propaganda coup, what had happened? I believe that Rainer Schmidt has it almost right. Except the SIS did not lure Hess to Britain, it invited him. To understand the context in which the deputy leader of Germany, in the middle of a war of survival with Britain, had reason to believe that he would be welcome here, we have to go back to the last months of 1939.
At that time, a substantial minority of Britain's leaders felt that the war was a tragedy. Some still admired Hitler. Others believed that there were powerful opposition groups in Germany anxious to overthrow Hitler and sue for peace and that these should be encouraged. The desire for peace, with or without the overthrow of Hitler, grew rapidly.
This wish was particularly strong in the SIS and it bombarded the Foreign Secretary, Lord Halifax, with reports of dissension in Germany. It pushed a policy of encouraging this dissent and "then see what happens". What happened was a disaster. The SIS believed it had made contact, through two of its officers in Holland, with a German group that wanted Britain on its side for an invasion of the Soviet Union. For a while the contact progressed, and there was even some agreement on peace terms - Hitler would remain in power for the time being; Austria, Czechoslovakia and Poland would be restored and there would be a united anti-Soviet front. Halifax approved all this and there was talk of a meeting in London to finalise matters.
On 1 November 1939, with the war two months old, the War Cabinet was told about these secret SIS negotiations for the first time - with some deliberate fudging by SIS on whether Hitler would be removed. The War Cabinet was far from happy, Churchill for one demanding that all contact with the Germans be broken off immediately.
In the end it was the Germans who terminated the operation. Himmler, the head of the Gestapo, who had with Hitler's approval authorised the contacts with the SIS, sensed his leader's second thoughts. German plans for an offensive against France and Britain were well advanced, Britain had spurned Hitler's offer of a compromise peace on 6 October; now further talk of peace smacked of defeatism. Himmler arranged a meeting with the two British SIS officers at the Dutch town of Venlo on the German border and there the Germans kidnapped them at gunpoint.
This was too much for Churchill and the moment he became Prime Minister in May 1940 he clamped down on all further peace feelers especially by the SIS - "Foreign Secretary: I hope it will be made clear to the [Papal] Nuncio that we do not desire to make any enquiries as to the terms of a peace with Hitler and that all of our agents are strictly forbidden to entertain any suggestions."
But there were Germans who still thought there was sufficient support in Britain for a compromise peace. Hess was one of them and when he arrived in Scotland he had with him a list of prominent British leaders who he believed would be sympathetic to his mission (see picture). Consider the effect if these names had become known at that stage of the war. The Germans had had a series of successes in North Africa and Greece. The U-boats appeared to be winning the Battle of the Atlantic. The Blitz was at its peak. Britain was running out of money to pay for arms from the United States, which was showing no signs of joining the war. According to the former American ambassador in London, Joseph Kennedy, Britain was finished.
President Roosevelt badly needed to know how strong Britain's stomach was for the fight. How would he have reacted if he had learnt that the Germans believed - rightly or wrongly - that some of Britain's leaders were ready for peace? What would such a revelation have done to his chances of persuading Congress to enter the war on Britain's side?
And what of the blow to our own morale if the British public were to learn the reason for Hess's mission, especially since so many prominent people were involved. No wonder the story was hushed up, no wonder Churchill decided to play down what could have been the propaganda coup of the war, no wonder successive governments have kept the lid on the affair.
In this secrecy lie the origins of many bizarre stories that have grown up about Hess - that it was not him but a double who landed in Scotland, that the SS intelligence chief Reinhard Heydrich intercepted Hess at Alborg in northern Denmark where Hess was either changing planes or refuelling, executed him on the spot for treason and then sent a trustworthy lookalike to test the extent of the plot.
Whether it is to protect the reputation of the compromise peace group, to suppress SIS involvement in the affair, to cover up Hess's possible murder, or some other conspiracy too complex to even guess at, the fact remains that there must be something murky in the British archives to embargo them for so long.
This is why some Germans think Hess deserves credit for a peace plan that, if it had come off, would have changed the course of the war and saved millions of lives. Many will not agree, but surely so long after that night in 1941 when British radar stations picked up Hess's Messerschmitt (but did nothing about it), the British public has the right to know the truth. The new open Labour government could release all the Hess files now - but do not count on it.