Jens,

Interesting hypothesis but I do not believe it would have led to greater losses for the Luftwaffe. They would have simply withdrawn earlier from the Battle after suffering approximately the same losses as historicaly recorded - just as they would if RAF fighters had been equipped with cannon.

Let us assume that a more efficient commitment by the RAF leads to an earlier withdrawal of the Luftwaffe by an improved margin of say four to six weeks.
The same determination to invade Russia would have still been there and such invasion would have taken place correspondingly earlier by whatever margin we fix.
The advantage to Hitler by this earlier invasion date would have brought the Wehrmacht to the gates of Moscow a crucial four to six weeks before they actually did - before General Winter froze the advance solid.
So, we can see that an earlier defeat of the Luftwaffe would not necessarily have been achieved by inflicting greater losses. In this scenario it actually leads to Hitler precipitating Barbarossa sometime in mid-May and ultimately entering Moscow before December 1941. Result: German victory throughout the eastern hemisphere.
Either way, the RAF Fighter Command operations over southeast England in the summer of 1940 prevented that victory in the east.