The radio telescope was officially invented in 1951. However, in 1911 Dr. Laurence Scarman invented a primitive form of this device, which he called a Marconiscope, which intercepted a signal from Mars.
In the 1970s, the Master attempted to use a radio telescope at Beacon Hill Research Establishment to transport his allies, the Nestene, to Earth as part of his plan to conquer that planet. (TV: Terror of the Autons)
A few years later, Dr. Louis French, a radio telescope director in Australia, developed and tested a radio wave accelerator in the hopes of making instantaneous contact with other planets. Instead, his device disrupted Earth's atmosphere, creating huge storms around the world, and devastated the planet Morrax. (COMIC: Is Anyone There?)
A former Cold War listening station in the English village of Goblin's Copse was repurposed into a radio telescope after the war's end. In 2009, it was used by the Tycho Project in their search for alien life, under the direction of Professor Nicholas Skinner. (TV: The Last Sontaran)