I don't think there is any argument that Hitler could have taken Britain. Hitler had the UTMOST respect for the Brits(as well as the Americans). I honestly think Hitler thought he had nuclear bombs coming in the near future, when the event you are speaking of happened.
Hitler probably figured why waste all of his resources bombing British civiilians that he respected in a small area heavily covered with AA batteries, if he had an insta-win in a few weeks? They have found high altitude Nazi air crafts that were taking pictures of New York for ICBM(inter continental ballistic missiles).
Hitler's warpath seems insane. Why not finish off the Brits? Why attack the Soviets so early in the war, before taking Europe? Why continue to fight until the end, and not surrender with no hope? Well all of these "anomalies" seem crazy, but can be explained by one thing. Hitler was VERY confidant in his future weapons program. He, for a period thought that he had OBVIOUSLY won the war. Methamphetamine, combined with his quick victories in Europe and Russia gave him over-confidence, as well as Technological Advantage(which he almost unarguably had).
I think it is likely that the USA somehow intercepted German nuclear materials, or bombs. This explains how the US, and Soviets both happened to figure out how to make nukes around the same time, both directly after the fall of the Nazis(and the plundering of Nazi Science sites). It also explains how the USA knew that their bombs would work. Apparently at the time Japan was bombed, we had never tested a bomb that big, or EVER tested a Plutonium bomb. We had no clue that they would work(that's the official story... we never tested a Plutonium bomb before Japan). Maybe we did know, somehow, even thought WE had never tested it(because we only used Uranium in our bombs... the NAZIS used plutonium).
Maybe the Nazis were close to completing a bomb than the USA(which makes sense, considering the Nazis were more advanced in nuclear science at the time than anyone else in the world). The USA caught up though, when they started to invade Germany. As they found German Nuclear sites(and as German Supplies cut off), the USA had FULL STEAM ahead, not being attacked at all all, allowing uninturrupted centrifuging of Uranium for bombs.
If Germany was not attacked, and having its supply lines cut off, and facilities destroyed(then looted by the US and Soviets), they probably would have had a nuke first. The only reason the US caught up is because we were not under attack, and could produce more Uranium because of it(and because we stole Nazi Scientists, during and after the war).