It is stated in The Green Death that the Prime Minister's Christian name is Jeremy. In the aftermath of several invasions of London in the late 60s, the 1970 election produces a hung parliament (conflicting Tory and Socialist policies towards the alien menace drive many voters towards the Liberals and fringe parties).
In this atmosphere, a coalition government, led by Jeremy Thorpe, governs Britain in the early 70s. However, the alien invasions continue, and with the power crisis caused by the collapse of Global Chemicals, the Government's involvement in the Axonite scandal (The Claws of Axos) and the Operation Golden Age fiasco, which included high ranking figures in the conspiracy (Invasion of the Dinosaurs), the government falls in early 1973, bringing the Labour party, with Shirley Williams as leader, back to power. In Terror of the Zygons the Brigadier addresses the Prime Minister as 'Madam'.