Pensioner Malcolm Baker told Mr Farron voters “did know” what they were voting for in the EU referendum and accused him of believing Leave supporters were racist.
The party leader was in the middle of a television interview in Kidlington, near Oxford, when the 65-year-old took him to task over his position on the EU.
Mr Baker said voters “do know, we did know” what they were backing in the referendum.
When Mr Farron insisted he did not believe Leave voters were racist, he replied: “Yes, you do. I tell you what, you keep going on all the time...”
Mr Farron questioned the disgruntled voter about whether he was proud his grandchildren “would inherit a poorer, less powerful, less secure country”.
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“I’m proud that they will be coming out of Europe and that we will have our own destiny and not have people telling us we are going to pay £100 billion to get out,” Mr Baker replied.
“If that’s your policies I hope you are going to get six seats.”
Mr Baker added: “I have always voted Labour but I will be voting for Theresa May.”
He later told the Press Association: “I’m fed up of hearing this chap keeping on running Britain down.”
Mr Farron said Mr Baker had only voted for Britain’s departure, not the final deal.
He told the Press Association: “We didn’t get round to the niceties of the argument. What Malcolm voted for was departure last June. I respect that.
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“He didn’t vote for destination, he wasn’t asked. None of us were asked.”
The Lib Dem leader said claims about clashes between the Prime Minister and EU Commission president Jean-Claude Juncker showed how the negotiations were playing out.
“The destination that we end up at ... we are getting some little clues from May and Juncker about what the next several months might look like, which will be ‘he said, she said’, pointless spats, lots of things behind closed doors, bits of which leak, and the end result imposed on the lot of us with a stitch-up,” he said.
“That is not democracy. So, for Malcolm’s sake and, dare I say, particularly for his grandchildren’s sake, that stitch-up must not be imposed on the British people.
“People should have the final say, not the politicians.”
He added: “If you believe in democracy and if you believe in the British spirit then neither of those things lead to you rolling over and dying when you have lost the result.”