Rex Farrel was the son of John Farrel and Mary Farrel. He took over as manager of Farrel Plastics after his father retired. The Master took control of him as part of his scheme to bring the Nestenes to Earth. After being defeated, the Master had Farrel disguised as himself and used him as a decoy to escape, leaving him to be shot and killed by Captain Mike Yates when he pulled out a gun. (TV: Terror of the Autons)
When Farrel took control of the industry, he invested most of its capital into machinery to replace handwork, disregarding advice from the chief engineer, George McDermott. He also invested in raw materials such as chemicals.
Farrel was very obedient to his father throughout all of his life and felt dominated by him. This made him more susceptible to the Master's hypnotising techniques. (PROSE: Doctor Who and the Terror of the Autons)