The rubbishest band in the history of rubbish

The answer to this is Sigue Sigue Sputnik. During the podcast intro of the show on 22nd January 2016 Mark got to play with a toy S.H.A.D.O. Interceptor from the TV series UFO. The firing of the Interceptor's single missile prompted the Good Doctors to start singing Love Missile F1-11 by Sigue Sigue Sputnik (which subsequently made it onto the Wittertainment Playlist). Mark was then heard to exclaim that they were "the rubbishest band in the history of rubbish".