Jo Brand is being investigated by police over an allegation of incitement to violence after she joked about throwing battery acid over politicians.

The Metropolitan Police said they had received a complaint about the BBC Radio 4 comedy programme in which Brand made her comments.

It came as Theresa May asked the BBC to explain why it had approved the joke for broadcast, suggesting that it “normalised” violence against politicians.

Brand had been referring to the recent milkshake attacks on political candidates, including Nigel Farage, on the Heresy comedy show. She said: “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.”