BBC Radio Leeds ran a news-related feature during Sunday’s breakfast show asking people to guess who the person was after listening to four songs as clues.
DJ Nathan Turvey, who was standing in for Radio Leeds’ regular Sunday presenter, played Mott The Hoople’s All The Young Dudes and The Brady Bunch theme song, followed by The Smiths’ Suffer Little Children, which was written in memory of the Moors murders
The last song played was The Talking Heads’ Psycho Killer.
The clip is hosted on Radiofail, a website featuring mistakes by DJs.
After playing the tracks, Turvey can he heard saying: “They were four songs all linked to someone in the news this week, all you’ve got to do is work out who it is.”
A BBC spokesman said: “This was clearly unacceptable and we apologise.”
Child-killer Brady, 79, died last week after spending half a century in prison for murders he committed with his partner Myra Hindley.