Henderson was the British ambassador to Germany in the years leading up to the Second World War, and he played a particularly important role in the negotiations that led to the Munich Agreement.
Henderson showed a willingness to capitulate to Hitler's demands to annex part of Czechoslovakia, as long as it protected Britain's interests. As he was heard to say at a private party in August 1938, "Great Britain would not think of risking even one sailor or airman for Czechoslovakia, and […] any reasonable solution would be agreed to so long as it were not attempted by force" (3.12.117). Obviously, he wasn't a fan of the Czechs, and Shirer believes that the final cost of the Munich Agreement was way, way too high.
Wilson acted as a British special envoy to Berlin during the negotiations that led to the Munich Agreement. Shirer describes him as having no experience as a diplomat and being too accommodating. Like the other British politicians who helped to bring about the Munich Agreement, Wilson seems—inexplicably—to have had little patience for the democratic Czechs, and plenty of patience for the totalitarian Nazis.
The Duke of Windsor (or, The Edward Formerly Known as King Edward VIII) plays a pretty small role in our story—even smaller than the one that he plays in The King's Speech, where he's portrayed by handsome Guy Pierce. But though his role in TRFTR is small, it's also pretty wacky.
The Duke had settled in France and fled to Spain, when Germany invaded France. was considered by the British government to be sympathetic to Hitler's cause. He had visited Hitler in Germany and seemed opposed to war. Probably because of his Nazi sympathies, the British government planned to ship him off to the Bahamas to become governor of that part of the Empire. The Nazis hatched a strange and mostly ridiculous plan to kidnap the Duke and stick him back on the throne—where, they assumed, he would reign in sympathy with Germany.
As you may have surmised, nothing much ever came of it.