Jo Brand has apologised for making a "crass and ill-judged" joke about throwing battery acid on politicians.
Appearing at the Henley Literary Festival in Henley-on-Thames, Oxfordshire, the comedian addressed controversy over her joke, in which she said that instead of throwing milkshakes, acid should be used.
But she reportedly told the audience she did not think that she had made a "mistake".
The Metropolitan Police announced yesterday that they were assessing the comments, following an allegation of incitement to violence
The joke has been criticised by both Brexit Party leader Nigel Farage and Prime Minister Theresa May, who called on the BBC to explain how it made it to air.
Mr Farage had a milkshake thrown over him during the European elections, and has been one of the biggest critics of Ms Brand.
He told talkRADIO’s James Whale he believed in free speech, but that Ms Brand crossed a line.
WATCH: Nigel Farage slams Jo Brand's battery acid joke
“If people are offended by what we say then tough, because we believe in free speech and liberty," he said.
“You do not incite violence. I believe that is exactly what Jo Brand did on that programme."
Mr Farage welcomed the police investigation into the comments.
“I also think that there are subjects that just aren’t funny - and the scourge of acid attacks that we have had in London is just not funny,” he said.
“The police should not spend much time on this. It is a clear cut case.”
The BBC said it regretted any offence caused by the broadcast, and it never intended to “encourage or condone violence”.
The comments will be edited out of future broadcasts.