How the Brits won the Battle of Britain

The time is 1940, early in WWII.  The Germans have just crushed the French, now the Third Reich owns all of Western Europe, except Britain.  The Brits managed to get the bulk of their army back from Belgium at Dunkirk.  They evacuated better than 300,000 men.  But they had to abandon all the army's heavy stuff, tanks, artillery, trucks, ammunition, supplies, yuge  amounts of stuff.  When Operation Dynamo ended, the British army, although back in England, was in no condition to fight. 
   If Hitler had managed to get even a small army across the channel and onto English soil, he would have owned the place.  The Channel is only 20 some miles wide at Dover and Pas de Calais.  Trouble is, the Channel is deep enough to float real warships, and the Brits had plenty of them.  If the Germans had loaded the troops onto Rhine River barges and attempted a crossing, the British would have steamed up along side with destroyers, and a few rounds would put the river barge and all its troops on the bottom.  At this time the Germans had only a hand full warships, less than a tenth of what the Royal Navy had. 
   Air power, the Luftwaffe, could have countered the Royal Navy.  To do this, the Germans had to wipe out the RAF.  They could not  sink or drive off the Royal Navy when they had Spitfires on their tails.  And so, the Luftwaffe attacked all that late summer and early fall of 1940.  Both sides had good pilots and good planes, qualitywise it was a draw between them.  The Germans had somewhat more aircraft but not a decisive margin.
    Fighter units can only generate so many sorties a day.  For instance my fighter wing in the Viet Nam war could do about 110 sorties a day from an assigned strength of 90 F105 Thunderchief fighter bombers.  We would launch 60 aircraft on the morning strike which got off at first light.  They would return around 11 AM.  We had until 2 PM to turn as many birds as possible , finish fixing broken birds from yesterday, and put together the afternoon strike of 60 aircraft.  I dare say RAF fighter squadrons could do a little better, the sorties being shorted and the aircraft had less high tech stuff to break and demand fixing.  (No doppler, no toss bomb computer, no radar, no TACAN, no gyro compass)  But I am sure they had a fixed number of sorties they could generate in a day. 
   The battle winning weapon the Brits had was radar, and a command and control system (the sector centers they were called)  that guaranteed that nearly all RAF fighter sorties would engage the enemy.  No sorties wasted patrolling, looking for the enemy, few or no sorties wasted when the enemy was not found.  Each sortie flow under radar control would find the enemy and score some kills.  This gave the RAF the winning edge in the summer of 1940.