Prime Minister of the United Kingdom

The Prime Minister was the political head of the United Kingdom. Several other nations had the same office title.

The Doctor spoke of having met and known then-Prime Minister Winston Churchill during World War II. (SP: Doctor Who: The Ultimate Adventure)

In the late 20th century Brigadier Lethbridge-Stewart consulted with a Prime Minister known only as "Jeremy". (DW: The Green Death) A few years later, he conferred with another, un-named female Prime Minister. (DW: Terror of the Zygons)

Margaret Thatcher presided as Prime Minister during the 1980s. (DW: Father's Day)

In early 2006, Great Britain has a male Prime Minister (possibly Tony Blair see Rise of the Cybermen). (DW: Aliens of London / World War Three) By Christmas of that year, Harriet Jones had taken over from him, though she earned the disfavour of the Doctor, who ensured her political downfall. (DW: The Christmas Invasion)

In 2008 Harold Saxon was elected Prime Minister. A few of the first things he did after coming into power was to gas his entire cabinet and to introduce the "Toclafane" to the human race. (DW: The Sound of Drums)

Other information
In the other Earth of Cybus Industries, Great Britain had the office of President rather than Prime Minister. (DW: Rise of the Cybermen / The Age of Steel)