Face of Nation : “Comedy will always push boundaries and will continue to do so, but on this occasion we have decided to edit the programme.
“We regret any offence we have caused.”
But fellow comedian Mr Baddiel, who created Heresy, said the BBC was wrong to edit the joke out of the repeat of the programme.
He told “I don’t think I would have nipped it out. Morally wrong? I’m not sure. I think they’re just trying not to cause trouble.
“The BBC are still to some extent the aunty of the nation and they don’t like trouble. Even though they did commission a show, Heresy, that was designed to push the boundaries of what people might think and say.
“If it was up to me, I would have kept that line in for the repeat. Apart from anything, it’s a bit silly when it’s had massive coverage to cut it out – that looks a bit cowardly.”
Last week, Mr Baddiel’s friend and long-time comedy partner Frank Skinner defended Ms Brand when he appeared on ITV’s Loose Women.
He said: “I think it is difficult to say anything in public life at all. When kids play Hangman, is that a devil may care attitude to capital punishment?
“I don’t think Jo, for one second, would want anyone to commit an act of violence – even against Nigel Farage.”
In reply to a question about the state of UK politics, Ms Brand had said on the Heresy programme: “Well, yes, I would say that but that’s because certain unpleasant characters are being thrown to the fore and they’re very, very easy to hate and I’m kind of thinking ‘Why bother with a milkshake when you could get some battery acid?’ That’s just me.
“I’m not going to do it, it’s purely a fantasy, but I think milkshakes are pathetic, I honestly do, sorry.”
She later apologised for the remark, calling it “crass and ill-judged”.
Last month, Mr Farage had a milkshake thrown over him while campaigning in Newcastle in the lead-up to the European elections.
He condemned Ms Brand’s words, and told news website Guido Fawkes: “This is incitement of violence and the police need to act.”
On Friday evening, police said Ms Brand would face no further action over the joke.
Scotland Yard said in a statement: “Police received an allegation of incitement to violence on 13 June, relating to comments made on a radio programme.
“The referral has been considered by the MPS and no further police action will be taken in relation to this allegation.”
