Cabinet unity has been stretched to its limits as Theresa May prepares for another critical round of Commons votes, with her ministers splitting over the prospect of a no-deal Brexit.

Justice secretary David Gauke said no deal would be “disastrous” and indicated he would quit his job if the PM took that route, but Brexiteer Andrea Leadsom insisted it was still on the cards.

On Tuesday Ms May will navigate a series of votes in parliament during which MPs will attempt to wrestle control of the Brexit process from her.

But on Saturday it appeared she may actually win a majority for a more supportive motion from a leading Conservative backbencher, which would see the party back her deal as long as the Irish backstop is renegotiated.

Asked if he believed it would be “pretty disastrous” for the UK to leave the EU without a deal, Mr Gauke told the BBC: “Yes, I do.”

He went on: “What I have said repeatedly is if there is a conscious choice, ‘right, that’s it, we’re going no deal’, when there are other options available, that would be something I would find extremely difficult.

“And, given the requirements of collective responsibility, then, obviously, I’d have to consider my position.”

Pressed on whether he backed MPs being given a free vote on extending Article 50 when alternatives to the government’s Brexit plans are debated on Tuesday, Mr Gauke said: “I think there is a case for free votes in this area to resolve things.”

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Chancellor Philip Hammond also declined to rule out quitting his post if the UK goes through with a no-deal Brexit.

Mr Hammond said it would cause “significant” disruption and damage to the economy, and that it went against what Leave voters had been told before the 2016 referendum.

But Commons leader Ms Leadsom stressed the need for cabinet unity behind Ms May’s stated position on a no-deal Brexit, while speaking on BBC2’s Newsnight.

She said: “I’m totally aligned to the prime minister. I believe that is where collective responsibility should lie.

“So number one, the legal default is we leave the EU on 29 March without a deal unless there is a deal is in place.

“That hasn’t changed. That is the prime minister’s view and that’s my view.”

Proposals likely to be put to a vote on Tuesday include one that would extend Article 50 and one to give parliament power over the Commons schedule instead of the executive, while another aiming for a second referendum was dropped due to a lack of support.