Therefore, its known narrative elements are not a part of the Doctor Who universe. It may have been the basis for a similar story in another medium, however — and that story may indeed be a part of the DWU.
- You may be looking for genesis of the Cybermen.
The Doctor and his companion "Felicity" arrive on the planet Mondas, Earth's twin orbiting on the opposite side of the Sun. While the Doctor works on a piece of TARDIS equipment, Felicity encounters the gentle Prince Sylvan. Sylvan accidentally activates the TARDIS, sending him, the Doctor and Felicity fifty years into the future. There, Sylvan's brother, Dega, is now king and has used the Doctor's device to begin turning his people into Cybermen. He has constructed a space fleet with which he intends to invade the mineral-rich Earth, and plans to kill any unconverted Mondans with cyanide gas. Felicity appeals to Dega's partly-Cybernised wife, Queen Meta, and she shoots her husband dead -- only to be killed by Dega's chief of staff, Krail. In the confusion, Sylvan and a band of Mondan rebels flee in the spaceships to Earth; the massive concussion of take-off knocks Mondas out of its orbit into deep space. 
Former Doctor Who script editor Davis submitted this idea circa early 1981, intending it to be a prequel to his and Kit Pedler's original Cyberman serial, The Tenth Planet (which also featured Cyberman Krail). Davis wrote his storyline with only the Doctor and one female companion in mind; he called this character "Felicity" rather than writing with any particular companion in mind.
Years later, Big Finish Productions would create a similar production starring the Fifth Doctor and about the creation of the Cybermen, called Spare Parts. World Enough and Time, a story in the 2017 series of Doctor Who told the "genesis of the Cybermen" on a Mondasian colony ship, but the next episode, The Doctor Falls, also established that there were multiple beginnings to the Cybermen, due to parallel evolution, therefore allowing for any number of previously-told Cybermen origins to coexist.