Nigel Farage was accused by the radio caller for "being wrong" about having to pay a Brexit bill during the referendum campaign.
The former Ukip leader strongly denied the claim and said Britain is “not hostages” to the European Union and is not entitled to pay anything to leave the Brussels bloc.
The radio caller infuriated Mr Farage when he said: “One is the exercise of power, which you’ve never had.
“The other one is reality, which is giving people the truthful message - which you never have.”
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We’re not hostages, we haven’t got to pay them a penny
Mr Farage appeared to grow increasingly frustrated as the radio caller continued and said: “All these promises you made in the referendum ‘we don’t have to pay anything to leave’ - you were wrong!”
In response, Mr Farage blasted: “We don’t have to pay anything to leave,”
“We’re not hostages, we haven’t got to pay them a penny, the fact our Prime Minister has agreed to is a separate issue.”
The LBC caller said: “Of course she has agreed to it because she recognises power as you don’t.”
He added: “You said that Trump would give us a trade deal within three months in January of last year, that’s nowhere near even starting.”
Mr Farage said: “Adrian, he wanted to do a trade deal with us.”
The caller said: “He didn’t. He failed.”
Mr Farage hit back: “Oh dear, dear, dear. Because our Prime Minister had to say ‘I’m sorry Mr Trump but we are not allowed to because the head master Barnier has said we can’t do this until much later on’.
“We are now supposed to be grateful that from April 2019 we can talk to Trump about a trade deal”
He added: “I absolutely refuse to accept that I told people in that referendum anything that wasn’t true.”
“Frankly, we should’ve just called it quits on the money.”
The European Union's chief Brexit negotiator Michel Barnier declared on Monday that a large part of the work has already been done for a Brexit deal including a "time-limited" transition period with the UK after he met with David Davis earlier today.
Mr Barnier said he and Brexit Secretary David Davis had made a “decisive step” towards agreeing a joint legal text on the UK’s EU withdrawal.
The Brussels negotiator also confirmed he would take the agreement to European Council of EU leaders for approval at Thursday's summit.