Hitler did not force the Luftwaffe to change targets to London. On the contrary, the war diary of the Wehrmacht High Command blames the failure to gain air superiority on the delay in permission to attack London:
"When the air fleet intended to go over to a large scale attack on London, the permission for such action could at first not be obtained but was given only after repeated urgent requests"
They then complained the weather had turned against them, robbing them of victory.
The truth is elements in the Luftwaffe had wanted to begin the BoB with an all out attack on London. They thought a large air battle would give the 109s the advantage, and after the RAF had been defeated in the air, they would be free to bomb their airfields with impunity. After the mauling they got in August (8% bomber losses), one of the 2 main air fleets was switched to night attacks, and it's fighters stripped to provide increased escorts for the other air fleet.
Even with that step, Luftwaffe strength was bleeding away. They had begun with 1,126 Bf 109 pilots at the end of June, 906 of them fit for duty.
By the end of September, even with the decrease in losses following the switch to London, they had 917 109 pilots, only 676 fit for duty.
In contrast, the RAF had 1,200 fighter pilots at the end of June. The figure is overstated because it includes Blenheim, Defiant and Gladiator pilots, and probably air gunners as well. However, by 7th September, the day the Luftwaffe switched to London, the RAF had 1,381 fighter pilots, an increase over the start of the battle. The following graph illustrates the trend, although it's mistakenly labelled single engined fighter pilots, it includes twin and obsolete types for the RAF:
In terms of aircraft, RAF frontline strength increased throughout the battle, and reserves were never exhausted. The Luftwaffe suffered a shortage of aircraft almost from the start, production unable to keep up with losses:
The Germans greatly overestimated their victories (about 3 to 1) and underestimated British production. For that reason, whilst they knew their own strength was declining, they thought British strength was declining faster. At times they believed the RAF had less than 200 Spitfires and Hurricanes left, whereas the true figure never went below 700.
The British overestimated their victories by about 1.5 times. However, they overestimated Luftwaffe strength and reserves, and hugely overestimated German production. That's why, in the brief period losses outstripped production, they thought they were losing. They believed the Germans were getting stronger, when they were actually getting much weaker.
