Jo Brand has apologised for making a joke about throwing battery acid at politicians, saying the comment was “crass and ill-judged”.
However, the comedian reportedly also said she did not feel she had made a “mistake” and that she had not mentioned Brexit Party leader Nigel Farage by name.
Mr Farage was among those publicly criticising Brand, 61, for the comment made on Victoria Coren Mitchell’s Radio 4 show Heresy on Tuesday, while speaking about recent protests in which milkshakes have been thrown at right-wing politicians.
The Met Police said on Thursday that it was assessing an allegation of incitement to violence.
Brand spoke out about the incident publicly for the first time later on Thursday, during a scheduled appearance at the Henley Literary Festival in Oxfordshire.
After arriving at the event, she sidestepped questions from Sky News but did say that freedom of speech in comedy was “extremely important”.
It comes as the BBC has said it will edit the programme following the backlash – including a call from Theresa May to explain why the joke was broadcast.
Watchdog Ofcom said it had received 65 complaints.
The comment was made during Brand’s appearance as a panellist on Heresy.
Asked about the state of UK politics, she replied: “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.”
Mr Farage, who was covered in milkshake during a campaign walkabout in Newcastle last month, said Brand’s comment was an “incitement of violence and police need to act”.
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?”
In its latest statement, 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 show.
Several social media users have compared the BBC’s response with Danny Baker‘s sacking over an alleged racist tweet about royal baby Archie – although Brand was a panellist on the show and not presenting.
Mrs May stepped into the row on Thursday, with her spokesman saying: “The prime minister has consistently said politicians should be able to campaign without harassment, intimidation and abuse.
“It is for the BBC to explain why it was appropriate content to broadcast.”
A statement from Scotland Yard said on Thursday: “Police have received an allegation of incitement to violence that was reported to the MPS on 13 June.
“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 complaint reported to the police is not believed to have been made by Mr Farage or the Brexit Party.
The trend of throwing milkshakes at right-wing politicians and activists began when viral footage showed Tommy Robinson being covered in Warrington.
Since then, several other members of the public have attempted to repeat the protest.
At the end of the Heresy show, Coren Mitchell said she hoped Brand’s remarks had not caused offence but added that the aim of the radio series was to “test the boundaries of what it’s okay to say and not say”.