The threat comes as the prime minister prepares to make a “bold offer” this week on the Withdrawal Agreement Bill in a last-ditch attempt to secure backing for Brexit plans.
As senior ministers jostled behind the scenes to replace the prime minister, Mr Barclay repeatedly refused to rule out standing in the looming Conservative leadership contest.
Speaking about the prospect of a no-deal scenario, the Brexit secretary said: “Members of parliament do need to face facts, and if the deal were not to go through then there are only two alternatives – you leave with a no deal or you revoke.
“If parliament won’t back a deal, I think we should bring forward our preparations to mitigate no deal, because we will need to use the additional time we have, and we need to move at pace to do so. We need to do more and use the additional time we have to prepare further.”
Last week, Mr Barclay said that if the Withdrawal Agreement Bill is defeated then the deal the prime minister thrashed out with the EU would be “dead”.
And he acknowledged the disruption a no-deal Brexit would cause, but claimed it was better than cancelling the UK’s exit from the bloc.
He said: “I think both options are undesirable but I think on no deal we would have to do all we can to mitigate the disruption – there would be disruption, and I have always been quite candid about that, which is why I think a deal is what we should be backing.”
During the interview Mr Barclay also attempted to laugh off questions about his own future ambitions, and repeatedly dodged questions.
Senior ministers, including Rory Stewart and Andrea Leadsom, have both publicly said they would consider running for the leadership, while former foreign secretary Boris Johnson topped a recent poll of the Tory grassroots to take over from Ms May when she stands aside.
Dodging the question, Mr Barclay replied: “I would say to my colleagues – focus on the day job, concentrate on what is before us, ensure we deliver on what we promised to the public, ensure that we leave.”
But just moments earlier, the defence minister Tobias Ellwood vented his frustration at Tory colleagues announcing their leadership ambitions, and urged “loyalty” and “discipline” to get Brexit across the line.
Asked about his leadership ambitions, Mr Ellwood said: “I don’t have the rank and I don’t have the experience. I’m not going to run. And this isn’t a TV reality contest.”
Mr Ellwood went on: “Let’s have some loyalty, let’s have some commitment, let’s have some discipline in focusing on the one thing that we need to get across the line, which is Brexit.
“The idea that we jump ahead and start toying around with who should be the leader... I do urge my colleagues to think why are they putting their name forward? Is it to raise their own profile? And some colleagues as well are changing their views in order to woo our membership to raise their profile as well.
“This is getting things in the wrong order. Our focus must be to get Brexit across the line.”