Mr Stewart, who won 19 votes in a surprise result, threatened to hold his own session of parliament across Parliament Square from Westminster if MPs are shut out of the Brexit process.
The international development secretary demanded that Mr Johnson be “straight” with the public about whether he was willing to prorogue parliament, after reports that the former Foreign Secretary has told some supporters he would suspend Westminster.
In public, Mr Johnson has said he is “instinctively averse to such arcane procedures” while pledging to leave the EU on 31 October come what may.
“I guarantee you, if he were to try, I and every other member of Parliament will sit across the road in Methodist Central Hall and we will hold our own session of Parliament and we will bring him down,” Mr Stewart said following yesterday’s result in the first leadership ballot of Tory MPs.
“Because you do not, ever, lock the doors of Parliament in this country or indeed in any other country with any respect in the world.”
He added: “Somebody who attempted to subvert our constitution, our liberties, our parliament, this place, who dared to stand as Prime Minister and claim they could lock the doors on Parliament would not deserve to be Prime Minister.
“And this Parliament would meet whether he locked the doors or not and we would bring him down.”
Mr Stewart claimed that “every Conservative MP with a very few exceptions would agree with me that an attempt to prorogue parliament would be unconstitutional and undermine the entire nature of our representative democracy.
“I would expect every one of them to be sitting with me in Methodist Central Hall holding a session of Parliament outside of this building if that man locked the door.”
Former Conservative chancellor Ken Clarke, who is supporting Mr Stewart’s leadership bid, became the latest Tory MP to claim he could quit the party if parliament is prorogued.
“I wouldn’t remotely support a prime minister staying in office who’s happy to contemplate doing that,” he said. Former Attorney General Dominic Grieve made a similar threat this week.
Earlier, Mr Stewart warned the UK risks being stuck in a political “zombieland” where no decisions are taken if parliament fails to pass a Brexit deal.
He said Parliament “won’t allow” the UK to leave the EU without a deal in place, adding Brussels would not allow the deal to be renegotiated.
Persuading MPs to back the existing withdrawal deal is the “only logical position”, he added.