Watchdog Ofcom says Radio 1 was in breach of guidelines when it broadcast swearing during live sets from Lily Allen and Ed Sheeran at Big Weekend.
Allen swore six times during her performance at the event in Glasgow in May, which was played out live between 1730 and 1800 BST.
Presenter Scott Mills warned listeners the sets may contain “strong language”.
But Ofcom ruled the offensive language was broadcast when “children were particularly likely to be listening”.
The BBC said when it did happen there was also an immediate apology.
It explained that a “comprehensive risk assessment” had been carried out and singers were told not to swear in writing, and on signs in their dressing room.
Ofcom noted that Sheeran swore during one of his songs at 1845 BST.
It added that as Allen was known to use strong language “it was reasonably predictable that her set could contain the most offensive language”.
Before Allen came on stage, Mills had issued the warning: “Now don’t forget this set may contain some strong language, it is live on Radio 1’s Big Weekend.
“We’re about to see Lily Allen. If you’re easily offended please go to the website and check out some other performance.”
The BBC explained it had considered cutting away from Allen’s set twice during her performance, but a senior producer decided to continue because apologies had already been given and it was believed that not that many children would be listening.
It also stated that in retrospect Radio 1 should have stopped broadcasting Allen’s set live after the second song that contained offensive language and edited the rest of her performance.