As Vaquero pointed out, when Hitler lost his nerve during the doomed British counterattack — it was made to buy time for the evacuation — he lost the opportunity to bag most of the British army in France. The British Navy would have been available, but the blow to morale, and the probable inability to defend the homeland from any German invasion, would have been a disaster for British morale. Churchill only remained as PM because literally no one else wanted the job — he was out on his ass ten weeks after victory in Europe.
And instead of the invasion of the USSR, Germany’s finishing up in North Africa would have cut off British access to Middle East oil — a blow to maintaining both the oil-burning British Navy as well as basic homefront needs — and destroyed most of what was left of the British army. That would have meant, no staging areas for an Allied return to Europe, and for the Germans, plenty of time to prepare for perhaps an eventual Barbarossa campaign.
The consequences for the Japanese would have been grim — had they gone ahead with their attacks on 12/7/41, they would have received our undivided attention, and cleaned out of the outlying islands including Okinawa perhaps two years earlier (tough to say, since US mobilization grew exponentially as it went on); invasion of the home island would have taken place, since there was no nuclear option until mid-1945.
The turning point in the Battle of Britain, was when in response to the Allied bombing of Berlin, Hitler turned to terror bombing of civilians, instead of strategic bombing of military targets....had he stayed the course, the Brits ability to defend from invasion probably would have been eliminated, while it was tragic in terms of the civilian toll, it gave the military some breathing space to repair their infrastructure.
I recall reading the first half of an alternate history book (cannot recall the name or author now - I left the book outside by the pool and and it got blown in). In this book, America did not enter the war because Japan did not attack Pearl Harbor, and the Nazis took Europe and the Middle East as you suggested. America became an island unto itself. A dark, depressed place where energy and other resources were scarce and there was constant fear of an invasion from all directions...