Rock band The Magic Numbers walked out of an appearance on TV show Top of the Pops because they thought the presenter made a joke about their weight.
The Magic Numbers had been due to perform their new single
In rehearsals, Richard Bacon said the band had been put in a "fat melting pot of talent" - and they left in protest at the "derogatory, unfunny remarks".
The group said they felt they had to "make a stand and leave".
But a BBC spokesman said Bacon tried to apologise and was referring to their status, not their appearance.
The Magic Numbers, who have been nominated for this year's Mercury Music Prize, were due to perform their new single Love Me Like You.
"It was an important day for us and should have been special," the band said on their website.
"We didn't take this decision lightly but we stand by it."
A BBC spokesman said Bacon used the word "fat" as a "figure of speech referring to the band's status".
"It was absolutely in no way referring the appearance of any of the band members," he said.
"Richard was mortified about the misunderstanding and any offence caused so he attempted to apologise personally to the band.
"However, their management denied him access to the band and they decided not to go ahead with their performance on the show."
The Magic Numbers, who released their eponymous debut album in June, are one of the UK's most acclaimed new bands.
Their place on the show was taken by electro-pop group Goldfrapp, who were in the studio at the time to record a performance for a future programme.