Rumours of a secret organistion called The Torchwood Institute have been circulating for a very long time amongst those who follow the likes of UNIT. However, very little about this organisation - should it even exist - is actually known.
The earliest mention of Torchwood dates back to the late Victorian age, when Queen Victoria is rumoured to have encountered a Werewolf whilst staying overnight at a place called the Torchwood Estate in Scotland. Assuming this tale has some basis in reality, it seems likely that Torchwood was set up by Queen Victoria either during these events, or as a response to them. Subsequent rumours about Torchwood place them as getting involved in many of the same kind of events that UNIT does.
Unlike UNIT, who are clearly tied into the structures of both the British Armed Forces and the United Nations, Torchwood would seem to be an independent organisation. If the Queen Victoria origin is true, then Torchwood may have an allegiance to the British monarchy, or covert links to the government.
Torchwood rumours seem to be tied primarily to specific geographical locations. If these rumours are correct, then Torchwood has bases in London, Cardiff, and Glasgow. Reports of London's Torchwood activities are often tied in to Canary Wharf and the Thames Flood Barrier, and reports from Cardiff suggest that they are based out of the bay area.