The Leader

The Leader, was a parallel universe was the President of the Republic of Great Britain and the third incarnation of the Doctor. (NA: Timewyrm: Revelation)

Biography
This universe's version of the Second Doctor selected one of the bodies offered to him by the Time Lords after his trial. Like his counterpart, this version of the Doctor was banished to Earth in the late 20th century, where he became President of the Republic. (NA: Timewyrm: Revelation)

The Leader may have been at least partly responsible for his Earth's much more advanced technology. He died in the volcanic catastrophe that struck Great Britain in the aftermath of I-Day. (PDA: The Face of the Enemy)

Behind the scenes
BBC special effects man Jack Kine "played" the part of the Leader on the Big Brother-liked posters seen during the course of Inferno. Inferno did not suggest that the Doctor and the Leader had any connection.