Final answer:
The British won the Battle of Britain due to effective radar technology, strong leadership from Winston Churchill, and the RAF's determination and home-field advantage, which outweighed the Luftwaffe's numerical superiority and led to the cancellation of the German invasion plan.
Step-by-step explanation:
The British were able to win the Battle of Britain for several key reasons. Foremost among these was the effective use of radar technology, which provided early warning of German air attacks, allowing the Royal Air Force (RAF) to better prepare and intercept incoming Luftwaffe planes. British pilots had the home-field advantage, as those shot down over Britain often survived and were able to return to combat, while German pilots were typically captured or killed. In addition, the leadership of Prime Minister Winston Churchill was instrumental in unifying and motivating the British people and the RAF to keep fighting against the advancing Germans. The RAF's determination, bolstered by new planes from British factories, and the assistance of pilots from other nations, outweighed the numerical advantage of the Luftwaffe's forces. Despite having fewer pilots and aircraft, the British managed to inflict significant losses on the German air force, preventing them from achieving air superiority, which was crucial for their planned invasion of Britain. Hitler's frustration at the Luftwaffe's inability to dominate the British skies led to the abandonment of Operation Sea Lion, the planned naval invasion of Britain.