The RAF won the battle because the -109's had notoriously short range. Imagine if the 109's could loiter for an hour or two over England.
Even more of them would get shot down.
The Luftwaffe lost the BoB because they couldn't shoot don enough RAF fighters, and they lost too many of their own fighters. Nothing to do with range.
In fact, if you look at the first phase of the BoB, the air fighting over the channel itself, the Luftwaffe lost that rather handsomely too. And that's when the fighting was only a few miles from their bases.
London is less than 100 miles from the Luftwaffe fighter bases in France. Most of the BoB was fought SE of London, closer to the Luftwaffe fighter bases.
Just to take a few days as examples.
15th August, heaviest days losses for the Luftwaffe. The Luftwaffe claims list shows they claimed victories at:
Folkestone - 13 claims, 24 miles from French coast
Calais - 1 claim. In France
Dover - 14 claims, 21 miles from French coast
Swanage - 2 claims, 65 miles from French coast
Clacton - 3 claims, 65 miles from French coast
There are scattered claims over Kent and the Channel, and some with no location listed. The only other major combats were over Portland, but they were by Bf 110s.
These aren't great distances, and the fact that the Luftwaffe was losing at this stage of the battle shows that it wasn't range that was their problem, it was the funamental fact that they weren't winning enough combats.
And the RAF would also be on the defensive, not sweeping the occupied countries within range, and the Luftwaffe would have been able to attack the bomber bases and disrupt them.
That didn't work out too well for them in 1940, and every year after that the odds tipped more heavily against them.
Noone ever won a war by remaining on the defense.
Tactically, the defensive is better, because you lose less. That's true in the air as well as on land. Strategically, of course, you have to go on the offensive to win, but the Germans simply didn't have the resources to do so (not even in 1940, although they didn't realise it)
It was the P38's and P51's rangin deep into Germany that broke the back of the Luftwaffe. It was not Spitfires flying over Britain that did it.
Well, as Williamson Murray points out in Strategy for Defeat, by the end of 1941 the Luftwaffe had already lost 2 complete air forces. He points out that that meant they had to hurry untrained pilots to the front. By the begining of 1942, only 60% of the Luftwaffe fighter pilots were operational, the rest didn't have the necessary training. Of the 107 German aces who scored more than 100 victories, only 8 went to the front line after mid 1942.
Murray goes on to point out that in May 1940, just before the invasion of France, the Luftwaffe had 1,369 fighters and 1,758 bombers. In Jan 1944 they had 1,561 fighters and 1,604 bombers. They faced, by 1944, a much larger RAF, and the addition of the USAAF and VVS.
As Murray sums it up:
"Further exacerbating this situation was the fact that the
Germans were forced to lower their standards for a fully operational pilot as the war
continued . There was, one must note, no decisive moment in this decline in
expertise. Rather as Winston Churchill has suggested in another context, the
Luftwaffe had entered the descent from 1940 "incontinently, fecklessly. . . . It is a
fine broad stairway at the beginning but after a bit the carpet ends . A little further
on, there are only flagstones ; and a little further on, these break beneath your
feet . "
The Luftwaffe began declining in strength relative to the opposition during the BoB. They never really recovered, and ended 1941 in a worse position than 1940, 1942 was worse than 1941, and so on.