Mr Stewart, a former Tory cabinet minister, said he worried about being seen as a political fraud but admitted he was not shy of putting himself centre-stage.
In an interview with Tatler, Mr Stewart said that the Microsoft co-founder and philanthropist “started arguing with me, and I noticed prickliness in myself.
“Unfairly, I felt that he felt that he was cleverer than me. And I noticed that I got wound up more quickly than I should have. One of my weaknesses is that I like to win arguments.”
The independent candidate said he was “clearly not vain about my sculpted upper body. But I am almost certainly vain about my mind.”
He added: “The thing I’m most worried about [in politics] is the accusation of fraudulence. I’m worried all the time that I’m treading a fine line between being potentially charismatic and exuberant, and playing the audience too much for cheap laughs or being too safe, because then you die as a person.”