Torchwood Four

Torchwood 4 is, or was, a branch of the Torchwood Institute. The nature of this branch, its location, and its personnel are at present unknown. According to information passed from Torchwood 3 leader Jack Harkness to new recruit Gwen Cooper, Torchwood 4 is lost, though there is hope it may be found one day. (TW: Everything Changes)

Behind the scenes
No further information regarding Torchwood 4 has, to date, been provided on screen. Speculation as to what and where Torchwood 4 was includes the possibility that it was the base at one time located under the Thames (DW: The Runaway Bride), or possibly the parallel Earth Torchwood on Pete's World (DW: 'Doomsday'').

Since there were/are Torchwood bases in each of the UK's countries; England (1), Scotland (2), Wales (3); perhaps Torchwood 4 is based in Northern Ireland. At the time of Torchwood's foundation in 1879, Ireland was still a part of the United Kingdom, and as such, it's capital, Dublin, would have been the most likely site of Torchwood 4's headquarters. The War of Independence (1919-1921) followed by the separation of southern Ireland from the UK might have had some role in the 'loss' of Torchwood 4.