Sam Mason, a presenter with BBC Radio Bristol has been sacked for asking a local taxi firm for a non-Asian driver to pick up her daughter.
The incident happened off-air, but after the transcript of the conversation appeared in the Sun newspaper, BBC bosses had to let her go.
The phone operator recorded the conversation and passed a copy of it to a journalist at the newspaper, who then asked the BBC to comment.
Sam was suspended on Friday but later dismissed.
The conversation reportedly went as follows:
Mason: "I know this sounds really racist, but I'm not being – please, don't send anyone like, you know what I mean. An English person would be great, a female would be better."
Operator: "We would class that as being racist. We can't penalise the Asian drivers and just send an English one." Mason: "You've managed it before."
Operator: "Right, OK. I don't agree with it personally."
Mason: "It's not your 14-year-old girl who's, you know, is it?" Operator: "Yes, but that's racist to say you don't want an Asian driver."
Mason: "If it were me I wouldn't care if it had two heads, but it's my little girl we are talking about."
After asking the woman to pass the call on to a supervisor, she finally adds: "I work at the BBC. I'm far from racist and that uneducated woman has no right to call me one. I don't want her to turn up with a guy with a turban on, it's going to freak her out. She's not used to Asians.
"She's not racist – her godparents are black."