Let's Put this Battle of Britain thing in Historical Context..

uhmmm I dunno fellas, there are a lot of things to keep into account..

Provided the Luftwaffe gained an air superiority on the southern part of England (cos that was the range of the fighters), it would still have been quite a feat to invade the UK from the sea.

Operation Overlord happened 4 years later and with an unprecedented logistic strain, something that the Germans would have never been able to achieve in 1940. Hitler's idea to look for a truce (he slowed down Guderian's advance in France and allowed the brits to leave relatively undisturbed from Dunkirk) was probably in view of the fact that an invasion of the UK was way harder that one might have thought and he was still sensible enough to understand it himself. It was no Operation Merkur, the UK is a big ass island

The only way would have been to use a massive amount of paras, establishing a bridgehead and slowly advance, but the bottleneck of the Channel link would have caused serious disruptions. If they didn't decide to do the foolish mistake of Barbarossa then MAYBE they could have managed an invasion, in hindsight it was easier to keep a truce with the Russians than trying to find a deal with Churchill, but hey, that's all guesswork.. fascinating pub topic though!