Presenter Dan Wootton called Lib Dem peer Lord Richard Newby "deluded" during a clash over whether there should be a second EU referendum.
Wootton insisted a second Brexit vote would "undermine democracy", but Lord Newby said democracy was the very reason he was calling for another referendum.
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"I've been involved in public life for a very, very long time. I'm a great fan of democracy, that's why I want people to have a vote," he said.
"I know you don't like polls, but that doesn't mean they're wrong. The majority of them want a vote, the majority of them now say if there was a vote they would vote to stay, so what you're saying is that the government should force through the biggest political decision in our lifetime against the evidence that people don't want it?".
'Why don't you listen to the Queen?'
Wootton accused the Lib Dem peer of trying to "destabilise the government", adding he thought it was "disgusting".
"Why don't you listen to the Queen and think about compromise for the good of the UK?," he said.
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Wootton said that polls were a "tiny little sample" of the population, which was not representative of the millions that voted in the original referendum.
"All I'm saying is that people now are faced witha series of facts which they didn't know at the time," Lord Newby said.