Meanwhile, remember Harriet Jones, who was Prime Minister (and appeared to have a good working relationship with Jack Harkness) until the Doctor took issue with her treatment of the Sontarans? Granted, the Master might have deposed her anyway — though he only managed to get to Earth via the Doctor’s TARDIS...
In other words, the Doctor’s actions played no small part in ensuring that when the 456 arrived, two key figures in power, the Prime Minister and Jack’s liaison with the Government, were men willing to destroy Torchwood and sell out the people they were supposedly sworn to protect.