Tony Blair

Tony Blair was a Prime Minister of the United Kingdom. (TV: Rise of the Cybermen) According to the Eighth Doctor, Blair served between Major and Clarke. (PROSE: Interference - Book One)

Harriet Jones joked that she wasn't one of "the babes", referring to the term "Blair's babes" for the female MPs that joined in his first government. (TV: World War Three)

Upon arriving in London of a parallel Earth in 2007, Mickey Smith suggested a possible difference being Tony Blair never getting elected. (TV: Rise of the Cybermen)

Jack Harkness suggested, perhaps jokingly, that Tony Blair was a Rutan spy in disguise. (WC: Monster Files)

Behind the scenes

In the non-canon Death Comes to Time, Tony Blair (unnamed but drawn & voiced as him) assured a confused US President that Britain had countermeasures. He then ordered an attack by a weaponised computer virus and UNIT space shuttles.
Prime Minister Terry Brooks in Millennium Shock is a pastiche of Tony Blair.
The appearance of Blair and a stammering Bush (voiced by Jon Culshaw) is a nod to the popularity of Culshaw's Bush and Blair sketches in Dead Ringers.
Jocrassa Fel-Fotch Passameer-Day Slitheen's claim that massive weapons of destruction could be launched on Earth in "45 seconds" (TV: World War Three) parodies Blair's claim that Iraq could launch weapons of mass destruction within 45 minutes. (Rose Tyler believes it will work, saying it did "last time")
On DVD commentary, producer Phil Collinson said that Aliens of London had intended to show a Blair look-a-like as the Prime Minister's corpse. When the resemblance proved disappointing, they decided to avoid showing the body clearly. Other hints and jabs at Blair remain, but the show avoids saying outright that he's the Prime Minister: the 2005 general election had not occurred during filming, and Rose and the Doctor are unaware who won so the show can avoid being in error.