Several candidates clashed over how to pass a deal to leave the European Union during a debate held on Sunday evening.
Michael Gove and Dominic Raab both claimed that they could win changes to the withdrawal agreement, which the EU says will not be re-opened.
“The fundamental issue here is that there’s a competition of machismo,” Mr Stewart said, to laughter and applause, as Mr Raab and Mr Gove spoke over one another.
“Everybody’s saying ‘I’m tougher’. Genuinely, genuinely, every time I have this debate everybody’s like ‘Trust me, I’m going to do it, I’m the guy, I can defeat the impossible odds’,” he added.
The Conservative MP then used an unusual analogy which amused the studio audience.
“It reminds me...I was trying to cram a whole series of rubbish bins into the...rubbish bin,” he said.
“And my wife said ‘you’re never going to get these three huge bags of rubbish in.
“And I was tempted, like Michael, like [Dominic], to say ‘believe in the bin! Believe in Britain! Right? It’s nonsense!”
Mr Stewart surprised Westminster when he survived the first round of voting in the Conservative leadership race, winning the backing of 19 MPs, which was more than expected.
Boris Johnson, widely considered the frontrunner in the race to replace Theresa May, refused to take part in Sunday’s debate, which was televised on Channel 4.