Presenter Evan Davis put it to Mr Farage that the British people didn’t really know what they wanted from Brexit.
But the Brexiteer champion hit back in fiery retort as he shut down Mr Davis’ suggestion.
He said: “I couldn’t disagree more. The Prime Minister has a huge mandate.
“It was called a referendum. It was the greatest exercise in democracy ever in the history of our nation – won by a very good, strong clear margin.
“Let’s just remind people that every single major player on both the Leave and Remain side of the debate said we will leave the European Union, the Single Market and the Customs Union – we couldn’t be any clearer.”
The Leave Means Leave chairman added: “There was a transition period – called Article 50 – of two years, through which all of this was to be sorted out.”
But Remainer Ken Clarke – who was also appearing on the programme, argued the UK needed much longer than two years to settle all the arrangements it needed to with the EU.
Mr Clarke also argued the UK Parliament was the biggest issue when it came to agreeing on a final Brexit deal.
He said “I have never known a more pathetic Parliament.
“The Parliament has so far failed to exercise any real influence over events.
“That is why you have referendums to neutralise parliaments and parties.
“Both parties are shattered and hopelessly divided – they can’t agree even among themselves.
“And you can’t get an agreement in Brussels which can get a majority in the Cabinet or can shut up the Brexiteers.
“Parliament has got to start functioning properly.”
He added: “In the end, we are a parliamentary democracy.
“I don’t think we should have decided all of this with one daft opinion poll.
“I want to see parliamentary democracy function properly.”