I can't believe the Evening Standard has taken the editorial line that Carol Thatcher didn't deserve to be sacked because she issued a blanket apology, when it is becoming clear she didn't apologise when personally confronted by people offended by her words at the time she said them.
The BBC is an employer. When it's employees are on the job, even in break rooms or in this case "the green room", they are required to meet certain requirements. One of these is to avoid using offensive or discriminatory language. If I were to refer to a famous black person whilst at work in my break room as a "golliwog" the company I work for would be entitled, and required, to begin disciplinary procedures against me. If I was as high profile as Carol Thatcher then perhaps those discipliary procedures would simply compromise getting fired.
It's an open and shut case. I believe in freedom of speech, on your own time, where it does not bring the consequences of your speech down upon your employer. At work one is bound to follow the rules that hold sway.