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

[MikeC1980]

Originally Posted by Al Schlageter

RAF BC would not be sitting idly by letting RAF FC do all the fighting. They would be attacking the beaches, the barges in the Channel and the ports in France, Belgium and Holland. The LW would have to dilute their fighter force to cover these threats.

That's why Hitler decided the Luftwaffe should wipe out the RAF before he would give the command to invade Britain. When the battle took longer than expected, and the favourable weather/season passed, Hitler's attention turned elsewhere.

Here are some good points I found elsewhere:

Germany couldn't defeat the British Air Force to the degree where they could have air supremacy. Invading a country without it is suicide.

Originally Hitler targeted only British airbases. Things were going well, at one point the English air force was down to only 200 planes.

Then a flight of German bombers accidentally bombed London. In retaliation Churchill ordered Berlin bombed. Hitler wigged it and ordered the destruction of London which gave the beleaguered RAF time to rebuild and change strategy.

After suffering heavy losses and causing little strategic damage to the British war machine the Germans finally gave up on the idea of invading England and turned their attention to the Soviet Union's oil fields, as Germany's oil supply was running low.