I believe that if Edward VIII was the king in WWII he would have probably supported the Nazis, and the UK with Ireland will help Nazi Germany to conquer all of Europe.
First, the annexation of Austria and the Sudetenland would go without any interruption from the UK, and so the conquering of Poland, Benelux and France.
Without the resistance of the UK Operation Barbarossa would've gone more well for the Germans, because there wouldn't be any need in operation Marita and the Balkan would be fully in their control (maybe not Yugoslavia, but the British could've handled that).
A Nazi Europe, with the UK support could've happen, so we need to thanks Wallis Simpson for being the woman she is, because she prevented a Axis victory in Europe.