Changing leaders mid term isn't unusual:
1902 AJ Balfour (Con)
1908 AA Asquith (Lib) - Won in 1910
1916 Lloyd George (Lib) - Won in 1918
1923 Stanley Baldwin (Con) - Won in 1924 and 1935
1937 Neville Chamberlain (Con)
1940 Winston Churchill (Con) - Won in 1951
1963 Sir Alec Douglas Home (Con)
1976 Jim Callaghan (Lab)
1990 John Major (Con) - Won in 1992
2007 Gordon Brown (Lab)
On that count three Conservatives and two Labour have become PM without an electoral mandate without having won either before or after.
You missed out Anthony Eden in 1955 (although he did immediately call an election) and Harold McMillan in 1957 (I think).
The staggering thing is that it took until 1975 for a Conservative leader to be elected, until then the leader was chosen by a secret committee of party bigwigs.