Kenneth Clarke

Kenneth Clarke was a Prime Minister of the United Kingdom. According to the Eighth Doctor, he immediately succeeded Tony Blair. (PROSE: Interference - Book One)

Behind the scenes
Clarke's forename wasn't given in Interference, but the common-sense interpretation of the passage is that the author was referencing the real-life Kenneth Clarke. (However, it's also possible that the reference was to .)

In real life, Clarke never became Prime Minister or Conservative Party leader.