I don't think the producer in question, Nic Philps, can be sacked by the BBC. He left the BBC a few weeks ago and works for Brand, who "produces" the show himself and then airs it on the BBC. Though I guess the BBC can and probably will halt his involvement in any future output.
I listened to the show when it originally aired - it's good to hear it context of the show each week might I add - and the reaction to this is ridiculous. Yes, it was offensive to Andrew Sachs, and that's about it. However suddenly it's Britain's beloved and cherished Andrew Sachs as opposed to "bloke with moustache who fell over a few times in Fawlty Towers". And it's "poor innocent girl exposed on the radio" as opposed to "girl who calls herself a 'Satanic Slut' and had sex with Russell Brand".
Her part in this is the worst for me. She's sobbing into every newspaper over her sex life and confidentially being divulged in public. Worth noting the two having sex was mentioned a week earlier without a response. Also that Russell Brand isn't exactly renowned for keeping these things under wraps. Moving on, quite why Gordon Brown et al feel it necessary to get involved is beyond me.
Again, the whole thing has been overreacted to. Ross won't be sacked, if Brand was it wouldn't hit him that hard, considering he's making movies and presumably drawing a lot more cash/fans from that. I suspect they'll be back, with increased listener numbers as a result. I wonder how many of these 18,000 compainees have ever heard the show outside of the 10 second clips shown on the news.