The rock band, which appeared on Radio 5 Live over a live link from the US, was heard uttering the line "F**k you, I won't do what you tell me" at least four times in the performance of 'Killing in the Name'.
The BBC presenter, Shelagh Fogarty, immediately apologised for the behaviour of the band. But many people complained to Ofcom that the performance was offensive and inappropriate for a breakfast show.
The programme editor also placed an apology on his blog, addressing the 32 people who complained directly to the BBC. The broadcaster has responded saying it had warned the band not to utter the original lyrics during the live performance.
Ofcom, which acknowledged the BBC's editorial justification, has appreciated its efforts to stop the band from using offensive language and its subsequent apologies for the occurrence.