Following the general election of 1935 Stanley Baldwin became Prime Minister. He resigned in May 1937 following the abdication of King Edward VIII. Neville Chamberlain was appointed Prime Minister by the newly crowned King George VI.
The General Election due in 1940 was cancelled due to the war. However, Chamberlain resigned as Prime Minister in May 1940 following a number of debacles early in WW2 which led to pressure for his resignation in the Commons. Winston Churchill then led the country�s wartime all-party government and was Prime Minister when the next General Election was held in 1945.
Sir Anthony Eden did indeed face the country shortly after taking over from Winston Churchill in 1955 (they did things differently in those days!). His party was returned to power with an increased majority of 59 seats.