The pair clashed while appearing on a live television debate after Mr Clarke, one of the most pro-EU members of the Conservative party, suggested Mr Farage was simply part of an “angry protest”.
The MP for Rushcliffe compared Ukip’s policies to that of other “simple” populist movements across Europe, such as Beppe Grillo’s Five Star Movement which played a starring role in the recent Italian referendum.
Speaking on Channel Four, Mr Clarke quashed recent suggestions of an EU implosion, saying: “The Italians are amongst the most pro-EU populations in Europe.
“The Italian vote was about lots of other things – they were protesting about the euro, which they blame for their economic problems.
“There is certainly a mood of angry protest throughout the Western world.
“I mean Trump, Nigel Farage, Beppe Grillo in Italy and others – they’re all different, country by country, but in common they have this angry anti-political establishment, life is very difficult, very complicated, simple solutions they are advocating.”
Mr Farage barked back insisting the political earthquakes of 2016 will continue until the European Union eventually folds.
He said: “It’s all well and good for Ken to talk in the terms that he does, but he’s missing something.
“We’re not just angry across the European Union, we’re recognising the failure of this project – whether it’s the eurozone, the migrant crisis, youth unemployment.
“Any measure you want – government from Brussels isn’t working and what is happening happened in Brexit, happened in Italy and almost happened in Austria with a genuinely far-right candidate.”
The Brexiteer refused to speculate on whether the European Union would actually collapse, but asserted his confidence the project had failed.
He added: “We’re watching the European project dying before our eyes and I’m very pleased about it because I didn’t just want the United Kingdom out of the European Union, I want Europe out of the European Union.
“I want a different Europe where friends – nation states – can trade and cooperate together, not have laws dictated to them and judged by a foreign court.
“It’s not a right-wing feeling, it’s not a left-wing feeling – it’s a very popular feeling.”
Mr Clarke responded by telling Mr Farage his opinions of the EU were “complete mythology”, claiming Britain will be weaker dealing with world issues like the migrant crisis without it in the future.
“The reality is we’re are better off if we maximise our clout in the world by cooperating with our neighbours,” he said.
“Poor old Ken, he’s a lovely bloke but he’s completely out of date,” Mr Farage fired back.
“The idea we are better off inside the European Union to operate with America – Ken, you may have missed this but a guy called Donald J. Trump becomes the President on January 20.
“And thank goodness for that, at last there’s a man in the White House who is pro-Britain, who wants us to have bilateral trade deal with America as quickly as possible and see’s an independent United Kingdom as a genuine bridge to the rest of Europe, and indeed, the rest of the Nato members.”