The President of Great Britain was the leader of Great Britain on two different parallel Earths.
On the Inferno Earth, two known British presidents were Gordon Lethbridge Stewart (PROSE: Night of the Intelligence) and an alternate Third Doctor (PROSE: Timewyrm: Revelation). Both led fascist regimes that harshly repressed dissent. (TV: Inferno)
On Pete's World, one President of Great Britain, who knew Pete Tyler, was in office in 2007. Following his deletion by John Lumic's Cybermen that year, (TV: Rise of the Cybermen) he was succeeded by Harriet Jones, who remained President into 2010. As in the primary universe, her time in office was referred to as "the Golden Age." The Tenth Doctor warned Pete Tyler to keep an eye on her, remembering her counterpart's actions with the Sycorax in his universe. (TV: Doomsday)