Labour MP Stephen Doughty clashed with talkRADIO host Mike Graham during a debate on whether the public wanted a second EU referendum.
Appearing on the breakfast show, Mr Doughty claimed he had received around 1,000 emails from constituents - including those who voted to leave - asking for a so-called People's Vote.
However, Graham argued the feedback he had heard from show listeners and social media users was that the public did not want a second referendum, and instead wanted "bloody politicians to just get on with it".
"Most people are fed up to the back teeth of talking abut Brexit. Most of the views that I hear are from people saying why can't these bloody politicians just get on with it. They don't want another referendum," Graham said.
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"You keep telling me you've had a thousand emails Stephen. I don't believe you."
The politician hit back, saying: "It's an absolute truth. You can't call me a liar on air".
"You want to tell me that my constituents who changed their minds are stupid?" he asked Graham. "I can tell you that this is the message that MPs are getting from all their constituents across the whole country. That's why areas like Wales that originally voted to leave now want to stay."
'I'm a liar and I'm ignorant - it's a great show isn't it'
The pair clashed again after Graham branded the politician "ignorant".
"So I'm ignorant now am I?," Mr Doughty retorted. "I'm a liar and I'm ignorant. It's a great show isn't it that you get to rant at me.
"This is the very problem that we've got with the media in this country. You don't want to debate the facts."