Deborah Cadbury discusses this incident in *Princes at War,* her book about the British royal family during World War II.
> To Hamilton’s amazement the mysterious parachutist now chose to reveal that he was none other than Hitler’s deputy: Rudolf Hess…. It became apparent that the enemy intruder was on a peace mission. Unnervingly for the duke, it was a peace mission in which it was presumed by the German before him that he himself would be an eager participant.
> This was all the more puzzling because he had not met Hess before, although Hess seemed to know a great deal about the duke. Hess had specifically targeted his family seat at Dungavel House as his destination…. Hess appeared to have made a concentrated effort that took many months of preparation to reach him. He said that he had tried to reach the Duke of Windsor in Lisbon the previous year. That plan had failed, but now, claimed the Deputy Führer intently, ‘he was on a mission of humanity’. He believed that there was a significant following in favour of peace in Britain and that the British aristocracy were in a position to oust Churchill and facilitate a negotiated settlement. ‘The Führer did not want to defeat England,’ Hess claimed, ‘and wished to stop the fighting.’
> The Duke of Hamilton found himself once again in a most delicate position. Hess’s actions appeared to imply he was a co-conspirator in a peace mission of breathtaking audacity. Furthermore, Hess’s story created the impression they had some kind of prior understanding. Hamilton, Hess believed, was an ‘Englishman’ who ‘would understand his point of view’, contact his family to say he was safe, and ‘ask the king to give him parole’. Hamilton did not hesitate. He escalated the matter not to the king , but directly to Churchill.
Hess seems to have believed himself to have a “connection” to Hamilton (who suffered accusations of being a Nazi sympathizer as a result). In the aftermath of Hess’ wild ride, the British government decided to release the news of his parachuting escapades to try to damage Nazi morale – either Hitler had endorsed his deputy’s audacious plan, in which case both could be painted as desperate, or he knew nothing of it, pointing to dissension and confusion in the upper echelons of the Nazi party. The Germans had declared Hess “mad” in their press, but that might have been cover; according to Cadbury, though, Churchill thought Hess might indeed have been “mad” with his devotion to Hitler:
> Churchill believed Hess was effectively undertaking a ‘deed of superb devotion’ to his hero, the Führer, who he worshipped, by sacrificing himself in his efforts to bring back for his leader peace with Britain.
British interrogators came to believe that Hess was indeed suffering from some form of psychosis:
> ‘Hess’s mental condition, which was somewhat masked before, has now declared itself as a true psychosis,’ wrote the army psychiatrist, Colonel Rees, on 19 June. Amongst his delusions was a conviction that there was a plot to poison him and an irrational overestimation of the importance of the Duke of Hamilton, a man who his ‘prophet friend’, Professor Haushofer, had marked out as a person ‘appointed by destiny’ to help his quest for peace. He ‘refused to be enlightened’ on his mistake and insisted ‘the king of England would never let these things happen’ if he was informed…. ‘We may have a mental patient on our hands permanently,’ warned Rees.
In short: fearful of failing his Fuhrer as Ribbentrop had, and emboldened by the Duke of Windsor’s ongoing flirtations with Nazism in Europe, Hess seems to have constructed a reality in which a significant portion of British leadership were willing to buy peace for the British Isles at the cost of Europe and decided to nobly sacrifice himself to bring about that end for Hitler.
Chapter 9 of Cadbury’s book goes into much more detail about this incident, including the Soviet response to what they saw as a very alarming possibility of peace between Germany and Britain.