Final answer:
Winston Churchill became the British Prime Minister during World War II after Neville Chamberlain resigned in 1940, due to Chamberlain's failed policy of appeasement with Nazi Germany.
Step-by-step explanation:
Winston Churchill, a lifelong British politician who had consistently warned against the rise of Adolf Hitler, was appointed Prime Minister of Britain during World War II after the resignation of Neville Chamberlain in 1940.
Churchill's leadership was marked by his determination to fight against Germany with all available means, a stance reflected in his famed speech where he declared, "I have nothing to offer but blood, toil, tears, and sweat." Prior to his appointment, Chamberlain's policy of appeasement, which included the Munich Pact that allowed Nazi Germany's annexation of parts of Czechoslovakia, failed to prevent the escalation of conflict, leading to his resignation.