The British electorate doesn't elect the Prime Minister: the PM is appointed by the monarch on the basis of who can control a majority of the House of Commons, which in practice (current events notwithstanding) usually means the leader of the largest party. In the case of the 1945 election, Churchill was personally popular, but his party, the Conservatives, were not.

By 1945, the Conservative Party had been in power for nearly ten years: the last election had been in 1935 and elections had been postponed for the duration of the war. The majority of Conservative MPs had not been advocates of rearmament as Churchill had been, rather, they were Chamberlainites who were strongly associated with the failed appeasement of Nazi Germany. The Conservative campaign was also weak, largely focused on the personality of Churchill as "the man who won the war". By contrast, the Labour Party campaigned on a clear and comprehensive platform of social reform, based on reconstructing the country and implementing the 1942 Beveridge Report, which advocated the formation of the Welfare State and National Health Service, in full. The Beveridge Report had been an immensely popular publication when it had been released, and while Churchill was sympathetic to its conclusions, the Conservative Party regarded it as unaffordable. The Labour Party had also earned a reputation for competence as part of Churchill's wartime coalition government: the Labour leader Clement Attlee had been Churchill's Deputy Prime Minister, Herbert Morrison had served as Home Secretary, and Ernest Bevin had been Minister of Labour, all positions that played to the Labour Party's strengths as the party of the working class.

Churchill himself had been prepared for an electoral defeat: numerous by-elections had gone badly for the Conservatives throughout the war, and he believed that the majority of the Armed Forces' vote would go to Labour. However, his personal popularity was still high and he was cheered by large crowds when he was on the campaign trail, which may have convinced him that the Conservatives would win. But the Prime Minister isn't a President and the election wasn't for him, it was for his party. Labour had a clear and optimistic message to restore the country after six years of war, while the Conservatives were associated with the failures of the past.

Sources:

Andrew Roberts, Churchill: Walking With Destiny