Here are two PODs from British political history:
1) The Conservatives under Benjamin Disraeli win the British general election of November/December 1868, instead of the Liberals under Gladstone. With the electoral pendulum alternating between Conservatives and Liberals, each party would be in power when they were in opposition in OTL, unless the pendulum becomes jammed on one side for two or more general elections.
2) John Clynes beats off the challenge by Ramsay MacDonald to the leadership of the Labour Party in November 1922. In OTL MacDonald beat Clynes by only 5 votes in the poll by Labour MPs. Assumimg that he becomes Prime Minister of a Labour minority government dependent on Liberal support in January 1924, as MacDonald did in OTL, he manages to keep the government in power for say up to 2 years. The Conservatives win the general election in the autumn of 1925. They lose the general election of 1930 because of the economic depression, and Labour under Clynes wins an overall majority. Because in OTL, Clynes was opposed to the formation of the National Government, this does not happen in this scenario. British foreign policy, particularly from 1935, could be different from OTL.