Jo Brand will not face police action after joking about throwing battery acid at politicians.
The comedian was reported over an allegation of incitement to violence after comments she made on the Radio 4 programme Heresy on Tuesday.
She later apologised for the joke, calling it “crass and ill-judged”.
Scotland Yard has now said Ms Brand will face no further action.
In a statement released on Friday, it said: “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 Metropolitan Police Service and no further police action will be taken in relation to this allegation.”
In reply to a question about the state of UK politics, Ms Brand had told the 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.”
Brexit Party leader Nigel Farage, who had milkshake thrown at him while campaigning in Newcastle, accused Ms Brand of inciting violence, although he did not say against whom.
Commenting again on Twitter, he said: “I am sick to death of overpaid, left-wing, so-called comedians on the BBC who think their view is morally superior.
“Can you imagine the reaction if I had said the same thing as Jo Brand?”
It is understood the report was not made to police by Mr Farage or the Brexit Party.
Broadcasting watchdog Ofcom said it received 65 complaints about the episode of Heresy.
The BBC said comedy would “always push boundaries”, but added that it would edit the Heresy programme, which is hosted by Victoria Coren Mitchell.
Comedian David Baddiel claimed the BBC was “cowardly” for censoring Ms Brand’s joke.
Speaking to Newsnight, he said: “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.”
Additional reporting by Press Association
