The Metropolitan Police has said it will take no further action over Jo Brand's comments on a radio show about throwing battery acid at politicians.
The comedian was accused of inciting violence after joking on BBC Radio 4's Heresy about throwing acid instead of milkshakes at "unpleasant characters".
She later apologised for what she called a "crass and ill-judged" joke.
The show's creator, David Baddiel, said the BBC was "cowardly" for removing the joke from a repeat of the episode.
Brexit Party leader Nigel Farage, who had milkshake thrown over him during the European election campaign in May, has accused Brand of inciting violence, although he did not say who against.
Writing on Twitter, he added: "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?"
In the episode of the Heresy broadcast on Tuesday, Brand told presenter Victoria Coren Mitchell that people who attacked "unpleasant figures" with milkshakes were "pathetic", adding: "Why bother with a milkshake when you could get some battery acid?"
The comic then went on to immediately make clear she was joking and criticised the milkshake stunts.
"I'm not going to do it," she said. "It's purely a fantasy, but I think milkshakes are pathetic, I honestly do, sorry."
Her follow-up comments were edited out of widely-shared clips on social media.
Ofcom said it received 65 complaints about the episode.
Appearing later at Henley Literary Festival, Brand said: "Looking back on it I think it was a somewhat crass and an ill-judged joke."
She added: "Nigel Farage tweeted the first bit that I said without the second bit when I apologised and said it was a joke and not something I would encourage.
"The current situation is I'm being chased around England and being asked if I feel I should apologise. I felt I apologised for it as I did it on the night. I'm a human being and people make mistakes. I apologise to all the people who I have offended."
The Sun said she added: "I don't think it's a mistake. If you think it is I'm happy to accept that.
"Female politicians and public figures are threatened day in, day out, with far worse things than battery acid... rape, murder and what have you.
"At least I'm here and trying to explain what I did. I don't think I have anyone to answer to. Nigel Farage wasn't even mentioned by me on the night so why he has taken it upon himself I don't know."
Mr Baddiel told BBC's Newsnight he did not think the BBC should have edited the joke out of a repeat of the programme.
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.
"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."
The broadcaster said on Thursday it regretted any offence caused and that, although comedy "will always push boundaries", the programme was "never intended to encourage or condone violence".
In a statement released on Friday, the Met 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 MPS and no further police action will be taken in relation to this allegation."