One Canada Square

One Canada Square in Canary Wharf in London was also known as Torchwood Tower. Circa 2007 it served as the headquarters of the Torchwood Institute.

History
The tower was built to reach the height of the radar black spot later determined by the Institute to constitute an anomaly in space and time, in reality a breach into the Void. The Torchwood Institute set out to investigate and, if possible, exploit the phenomenon. The true nature of the tower and the existence of Torchwood itself would remain unknown to the public. Torchwood 1 would later base itself out of the tower. (DW: Army of Ghosts)

Though this seems contradictory in light of that information, Tobias Vaughn's former associate Ashley Chapel, the designer of the micromonolithic circuit, operated his company, ACL, of the tower in late 1999. Due to Chapel's use of the Millenium Codex, the tower briefly entered or transformed into the Great Kingdom where One Canada turned into the Tower of Abraxas. (MA: Millennial Rites)

Other sections of the Tower acted as testing grounds for technology derived from alien artefacts. Torchwood was involved in experimental "ghost shifts" which opened up the Void and allowed the Cybermen of another world to enter this universe. A golden levitating sphere, actually a Void Ship, appeared at the spot. The Void ship contained the Cult of Skaro, Dalek leaders originally from this universe, who had escaped into the Void to survive the Last Great Time War, who clashed with the Cybermen in the conflict known as the Battle of Canary Wharf. The Doctor discovered a way to make it so that anything touched by the Void would return there. This included millions of Cybermen from the other world as well as every Dalek that had come through the Void. This, as well as the battle itself, caused great damage to the building. (DW: Army of Ghosts / Doomsday)

Other information
Ianto Jones and his lover, Lisa Hallett, both of whom worked for Torchwood 1, both managed to escape from the buidling. before its destruction. Lisa, at this stage, had already gotten partially cyber-converted. (TW: Cyberwoman)

Alternate timelines
In an alternative 2006 in which London lies in ruins, the British Army based itself out of the tower. (PDA: The Time Travellers)