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.

20th century
The Doctor spoke of having met and known then-Prime Minister Winston Churchill during World War II. (He would also act as a consultant to Margaret Thatcher. 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, unnamed female Prime Minister. (DW: Terror of the Zygons)

On 6 May 1997, the Prime Minister, a man, is assassinated by his own bodyguard while in Washington during the Lord Xznaal crisis. (NA: The Dying Days)

21st century
In early 2006, the United Kingdom has a male Prime Minister who is killed by the Slitheen. The position of Acting Prime Minister is then assumed by Joseph Green, who is actually Jocrassa Fel-Fotch Passameer-Day Slitheen wearing the slain Green's skin. Jocrassa and his brothers are later killed by a missile strike on 10 Downing Street. (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. Shortly after his election, he gassed his entire cabinet and introduced the Toclafane to the human race. (DW: The Sound of Drums)

During the 2009 Dalek invasion, Gwen yells to Jack that they have lost contact with the Prime Minister's plane, making it seem likely that this was the person to replace Harold Saxon but that they are now dead. (DW: The Stolen Earth)

Alternate timelines
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)

1940s

 * Winston Churchill

1980s

 * Margaret Thatcher

2000s

 * Tony Blair (possibly pre-2006) - mentioned by Mickey Smith (DW: Rise of the Cybermen), probably Harriet Jones' predecessor whom the Slitheen killed. (DW: Aliens of London) Following the Slitheen crisis, his death was officially deemed an accident. (whoisdoctorwho.co.uk)
 * "Joseph Green" (acting 2006) - Slitheen in disguise. (DW: Aliens of London/World War Three)
 * Harriet Jones (2006-08) (DW: World War Three, The Christmas Invasion, The Stolen Earth)
 * "Harold Saxon" (2008, negated timeline) (DW: The Sound of Drums/Last of the Time Lords)
 * Unknown Prime Minister (2008 - 2009) who presumably took over from Harold Saxon (SJA: Revenge of the Slitheen) and was apparently killed during the Dalek invasion when the plane he or she was travelling on was lost. (DW: The Stolen Earth)