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, un-named female Prime Minister. (DW: Terror of the Zygons)

21st century
In early 2006, Great Britain has a male Prime Minister who is killed by the Slitheen. (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 to introduce the Toclafane to the human race. (DW: The Sound of Drums)

In The Stolen Earth Gwen yells to Jack that they have lost contact with the Prime Ministers plane making it seem likely that this was the person to replace Harold Saxon but that they are now dead.

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), likely to have been a continuity error confusion caused by the real life British Prime Minister at the time. Though it could possibley have been Harriet Jones' predecessor whom the Slitheen killed. (DW: Aliens of London)
 * "Joseph Green" (acting 2006) - Slitheen in disguise. (DW: Aliens of London/World War Three)
 * Harriet Jones (2006-07) (DW: World War Three, The Christmas Invasion, The Stolen Earth)
 * "Harold Saxon" (2008-09, negated timeline) (DW: The Sound of Drums/Last of the Time Lords)
 * Unknown person mentioned in The Stolen Earth as having lost contact while on a plane presumably this person took over from Harold Saxon and is dead now.