A factory was a place where items were manufactured.
Wildthyme Unlimited was a factory in England in which Iris Wildthyme manufactured Suitors for her company, Suitors, Inc.. The robots were designed to resemble either the Fourth or Third Doctor. (PROSE: Suitors, Inc.)
The Bane made Bubble Shock! in their London Bubble Shock! factory. This was part of their plan to convert all of the human race into Bane zombies. The factory was destroyed in 2008. (TV: Invasion of the Bane)