Battersea Power Station was located in the city of London.
History
In Normal Space, by the time of the 22nd century Dalek invasion of Earth, to the surprise of Ian Chesterton and Barbara Wright, who came from the year 1963, it had been converted into a nuclear power plant and was visibly different to the power station that they knew, as two of the chimneys were damaged. (DW: The Dalek Invasion of Earth)
Parallel Earth
In a parallel Earth, the station no longer served its original purpose. Cybus Industries employed it as a Cyber-conversion centre and base for the Cybermen created by John Lumic. The factory was converted from the inside and deep inside its structure, thousands of Cyber Conversion machines went to work, cutting out the brains of London's population, through this means 'upgrading' them. It was here that Mr. Crane and his men created the first Cybermen before Lumic's arrival.
When London was taken over by the Cybermen, Lumic took full authority over his factory but it was soon given to the Cybermen when they upgraded him. Soon after, the Tenth Doctor and his allies gained access to the factory and were led to Cyber Control where they met the upgraded Lumic, the Cyber-Controller.
It was destroyed when the Doctor used Rose Tyler's superphone to send a signal which destroyed all the Cybermen inside. The entire building was engulfed in flames and the Doctor and his friends made a lucky escape from it in the Cybus Industries Zeppelin. (DW: The Age of Steel)
