Speaking on Radio 4 panel show Heresy on Tuesday night, the comedian was asked if Brits are “absolutely united in feeling we are living through a terrible time” with the ongoing divisions around Brexit.
Brand replied: “Well, yes I would say that but I think 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?’”
The response drew laughter on the show but Brand quickly added: “That’s just me, sorry, I’m not gonna do it, it’s purely a fantasy, but I think milk shakes are pathetic, I honestly do. Sorry.”
Milkshaking became an overnight sensation earlier this year when a number of political figures including Farage and Tommy Robinson were drenched in the beverage while walking the streets of the UK.
Farage, who was hit with a milkshake in Newcastle last month, reacted furiously to Brand’s comments.
In a tweet, he said: “This is incitement of violence and the police need to act.”
At the end of Tuesday’s Heresy show, host Victoria Coren Mitchell said she hoped Brand’s remarks had not caused offence but stressed the programme was all about “test[ing] the boundaries of what it’s OK to say and not say”.
She later replied to Farage’s tweet, saying: “Nigel! I’m genuinely disappointed; we don’t agree on everything, but I would totally have had you down as a free speech man.
“Especially when it comes to jokes.”
In may 2017 Farage has said he would “don khaki, pick up a rifle and head for the front lines” if Theresa May failed to deliver a Brexit he was unhappy with.
Broadcasting watchdog Ofcom said that, as of Wednesday afternoon, it had received 19 complaints about the episode in question.
A BBC spokeswoman said: “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.”