Speaking at The Independent’s Indy Brexit Debate in London, Ms Miller suggested the 2016 Brexit referendum was too complex a question to be voted on.
The businesswoman and activist said: “You should never have given a very complex question to the people of Britain.
“You should have never put the people of Britain in this position; you should never have done it.”
Conservative MP Jacob Rees-Mogg retorted sharply and rejected Ms Miller’s calls for a second referendum at the end of the Brexit process.
He said: “There is the fairly obvious point, how come the British electorate were too stupid to know how they were voting between a first and second referendum.”
Ms Miller rejected Mr Rees-Mogg’s statement, claiming he had “put words” in her mouth.
However the Conservative MP said the decision of the British electorate at the 2016 referendum should be trusted, as is the case with typical General Elections.
He said: “General elections are complicated but actually we trust the British public to make the right decision.
“They don’t necessarily read through every page of every manifesto, but they make their decision and that is legitimate in itself.
“The referendum was likewise a legitimate decision by people who had participated in the debate and we had a turnout that was higher than any General Election since 1992; people were interested and engaged.”
He concluded: “They voted to leave, they didn’t vote to find they were tied in by second degree or they were given a Brexit which meant they were still subject to EU rules.”
However Ms Miller argued that the British electorate must be given a second vote on the final deal reached in Brussels and accused the Government of failing to acknowledge the nuanced nature of Leave voters.
She said: “We come to the idea that this is what people wanted.
“How on earth do you actually know what was in the minds of people when they voted; stop talking about things you have no idea about.”
She called on the MPs to allow the British public to “validate” the final Brexit deal following the conclusion of the ongoing negotiations.
She said: “Let’s see what Mrs May can come back with and then ask the people again to validate it.
“Just ask them again is this is what you want? Why is that so complicated.”
Attacking the Conservative MPs on the panel in particular, she added: “Stop scoring political points on all of this; it’s really not helpful.
“This is about people’s real lives, this is not about your seats or your powers or the fact that you are spending our money.
“I’m sorry, you’re wasting my money as a taxpayer and everyone’s in this audience. Stop it.”