Nigel Farage has demanded police take action against Jo Brand for "incitement of violence" after the comedian joked about throwing battery acid at politicians.

During an appearance on BBC Radio 4's Heresy, the comedian was asked by host Victoria Coren Mitchell about the "terrible" state of British politics.

She 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?"

As the studio audience laughed, the 61-year-old added: "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 subsequently denounced the comments on Twitter.

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"This is incitement of violence and the police need to act," the Brexit Party leader who was hit by a milkshake last month in Newcastle city centre during the European Parliament election campaign.

After the incident he was heard to comment "complete failure" as he was ushered away by security. "I could have spotted that a mile off"

The trend of throwing milkshakes at right-wing politicians began when Tommy Robinson had one thrown over him in Warrington, during his failed election campaign.

Several other members of the public have since then, attempted to repeat the unusual protest.

At the end of show, Coren Mitchell said she hoped Brand's remarks had not caused offence but added that the radio series had been set up to "test the boundaries of what it's OK to say and not say".

The 46-year-old later accused Mr Farage of double standards on Twitter.

"Nigel! I'm genuinely disappointed; we don't agree on everything, but I would totally have had you down as a free speech man," she wrote. "Especially when it comes to jokes."

A BBC spokesperson: “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.”

Mr Farage has himself been forced to deny encouraging violence after he told an audience in 2017 he would "don khaki, pick up a rifle and head for the front lines" if Theresa May failed to deliver Brexit.

Nigel Farage filmed saying he might have to arm himself and join the frontline if Brexit is thwarted

A spokesman for the then-Ukip leader later said his comments were taken out of context and that the part was "opposed to any type of violence".

Mr Farage's complaint also contrasts to a claim he made in his 2010 autobiography, Fighting Bull.

"Freedom of speech and belief is not subject to approval by a transitory authority. It is absolute or it is nothing," he wrote. "Such was and remains my conviction. And oh, it has got me into some delicious trouble."