It has been reported that the Metropolitan Police Force is assessing the "battery acid" joke made by Jo Brand on the Radio 4 comedy Heresy following an allegation of incitement to violence.

A spokesperson for the Met said: "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."

Brand has been asked if she would continue working with the BBC and she is reported to have replied: "I'm not employed by the BBC, so how can they sack me?"

Brand said on the first edition of the new series on Tuesday: "...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?'" and then followed it up by clarifying that she was being satirical: "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."

Following a complaint from Nigel Farage that "the police need to act" the BBC said of the show, which was created by David Baddiel, "Heresy is a long-running comedy programme where, as the title implies and as our listeners know, panellists often say things which are deliberately provocative and go against societal norms but are not intended to be taken seriously."

Nigel Farage also tweeted: "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?"

The joke continues to cause controversy. Some people have circulated the initial remark without the part where she said she didn't mean it. Others have pointed out that the BBC did not defend Danny Baker when he posted his controversial tweet – instead he was sacked. Others have condemned Brand yet have been accused of being the kind of people who demand the right of free speech.

Today (Thursday) a spokesman for the Prime Minister has said: "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."

The joke has now been edited out of the programme on the BBC's catch-up service.