A joke. Well, that's ok then, isn't it? Of course not - you just cannot use language that you know is offensive, especially while at work. Just because Thatcher wasn't broadcasting at the time is no excuse - she was there as a representative of the BBC, in their employment, and should have acted accordingly. As BBC1 controller Jay Hunt said,
What Carol decides to say in the privacy of her own home or in a private conversation with friends is one thing. What she says in a green room space, when there are 12 people, in her capacity as a roving reporter for The One Show is a rather different thing.
Clearly the remarks were not made in private - they were in a corporate workspace, akin to an office environment, and when in such a place a certain decorum is sorely needed. As for the "innocent joke" thing, well that's fine if it's true. But if you're making a genuinely innocent joke and you accidentally make a faux pas and actually offend someone, then you jolly well apologise for it. The BBC1 controller said that the main reason why Thatcher was sacked was not so much for the remark itself, but for her lack of remorse:
What I find sad about the entire situation is that we have given Carol ample opportunity to apologise for offence that was caused to key named individuals.
"She felt unable to do that and, for that reason, it is not appropriate for her to work on that particular show, but she will continue to work for the BBC and indeed is.
Sounds more than fair to me.