One other thing I've been pondering is Harriet Jones. There is of course the 'If the Doctor hadn't deposed her, things would have turned out differently', which is most probably true.
The thing is, I can't see how Harriet Jones would have been PM by the time the 456 arrived even if the Doctor had handed her flowers and congratulations at the end of The Christmas Invasion instead of saying those seven words. Had Harriet been at the height of her popularity and in power when the Master came to Earth, he'd simply have assassinated her (by proxy, most likely) because becoming PM was essential to his plans and he wouldn't have led something like a popular PM stand in his way. He probably would have been the first to hold heartfelt speeches about her martyrdom and get elected as her avenger, or something. Which still would have meant Brian Green as PM later on.
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The thing is, I can't see how Harriet Jones would have been PM by the time the 456 arrived even if the Doctor had handed her flowers and congratulations at the end of The Christmas Invasion instead of saying those seven words. Had Harriet been at the height of her popularity and in power when the Master came to Earth, he'd simply have assassinated her (by proxy, most likely) because becoming PM was essential to his plans and he wouldn't have led something like a popular PM stand in his way. He probably would have been the first to hold heartfelt speeches about her martyrdom and get elected as her avenger, or something. Which still would have meant Brian Green as PM later on.