Mr Smith, an advocate of a hard Brexit, has taken a swipe at “establishment losing the plot” over leaving the EU.
He told LBC’s Andrew Castle that Remainers would be faced with “huge public anger” if they dared pushed through a “betrayal” of the 2016 vote.
Mr Smith said: “I don’t think there is any desire in any way for having another fractious referendum. The last referendum was an experience enough.
“I don’t think people want to go back through that process. I don’t see what all of this is about.
“When you ask people a question and people vote in a democracy, you don’t get to ask them the same question again and again and again on the same decision, until the people who want to Remain get what they see as the right answer.
“I think a second vote would lead to huge anger amongst many in the public who feel like they’re being betrayed.
“That they were asked a question, and because the answer they gave wasn’t satisfactory to the establishment, who seem to be driven mad by this vote, they are losing the plot – they can’t understand what life is like outside the EU, that is not a reason to hold a referendum.
“The referendum was: Should we leave? The answer was yes. The best deal is the one we can leave on.
“The reality is we need to get the arrangement that best reflects what leaving means – taking control of borders, laws and money.”
The Brexiteer’s scathing rebuke of a People’s Vote come as London mayor Sadiq Khan called for another Brexit vote, saying that the British public should get a “fresh say on our future”.
Mr Khan said the referendum should offer voters the choice of staying in the EU against any deal the government manages to strike – or a no-deal if talks fail.
The latest push from one of Labour’s most powerful figures will likely increase the pressure on Jeremy Corbyn ahead of the party conference next week.
There are already more than 100 anti-Brexit motions submitted, including calls for a new vote on the final deal.
Among the Brexiteer wing of the Tory party, there is a growing movement urging the Prime Minister to “chuck Chequers”.
Former Brexit minister Steve Baker has warned Mrs May that up to 80 Tory MPs are prepared to vote against Theresa May’s Chequers plan.
Despite criticism from within Mrs May’s own party, No 10 confirmed its plan was the “only one on the table” able to deliver on the will of British people while avoiding a hard border.
The Chequers agreement in July triggered the cabinet resignations of both David Davis and Boris Johnson.
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