Torchwood Two
Torchwood Two was one of the Torchwood Institute's four main bases in the 2000s. It was located near the waterfront development on the River Clyde in Glasgow and run by "Old Tartan Archie" (PROSE: The Twilight Streets) By 2016, all branches of Torchwood were inactive due to unfortunate events. (AUDIO: More Than This)
History
Torchwood Two was formed by Archie, who chose to leave Torchwood One to form a new branch in Glasgow. (AUDIO: The Torchwood Archive)
Torchwood Two was well-connected to Torchwood Three, since they contacted Captain Jack Harkness to come to Scotland in connection with a number of deaths in a pub. (COMIC: Captain Jack and the Selkie)
According to files in the possession of the British government, Torchwood Two was assumed to have been disbanded at some point prior to the 456 crisis, which took place in September 2009. (TV: Children of Earth: Day Two) Gwen Cooper claimed in 2016 that all branches of Torchwood were inactive. (AUDIO: More Than This)
Behind the scenes
The implication of Jack's televised line, "Torchwood Two is an office in Glasgow; very strange man", is that that office is comprised of a single individual. However the reference in COMIC: Captain Jack and the Selkie offers no such implication. There, he says that he was simply "contacted by Torchwood Glasgow" and makes no mention of any individuals.