Jo Brand is to face no further police action over a joke she made about throwing battery acid on politicians.
Her remarks on the BBC Radio 4 programme Heresy on Tuesday night led to public criticism, including from Brexit Party leader Nigel Farage, and multiple complaints being made to broadcasting watchdog Ofcom.
The Met Police was assessing Brand's comment following an allegation of incitement to violence.
The force said in a statement on Friday evening: “Police received an allegation of incitement to violence on June 13, 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.”
Appearing at an event in Henley, Oxfordshire, earlier today, the comedian apologised for making a "crass and ill-judged" joke.
But she reportedly told the audience she did not think that she had made a "mistake", adding that she had not mentioned Mr Farage.
On Wednesday, the Brexit Party leader, who had a milkshake thrown at him while campaigning in Newcastle, accused Brand of inciting violence, although he did not say who against.
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?"
Ofcom said it has received 65 complaints about the episode of Heresy.
A statement from Scotland Yard said on Thursday: "Police have received an allegation of incitement to violence that was reported to the MPS on June 13.
"The allegation relates to comments made on a radio programme. The allegation is currently being assessed.
"There have been no arrests and inquiries are ongoing."
The allegation reported to the police is not believed to have been made by Mr Farage or the Brexit Party.
A spokesman for Prime Minister Theresa May called on the BBC to explain why it broadcast Brand's comments, saying that "violence and intimidation should not be normalised".
The BBC said it regretted any offence caused by the radio programme, which was never intended "to encourage or condone violence".
The corporation said comedy would "always push boundaries", but added that it would edit the Heresy programme, which is hosted by Victoria Coren Mitchell.
In reply to a question about the state of UK politics, 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."
