Mr Gauke stepped up his efforts to stop the UK crashing out of the EU without a deal, saying it would be “very difficult” for him to stay in the cabinet if that course is taken.
Significantly, he widened his criticism to argue Ms May would face too much opposition – although he did not say whether he meant in the cabinet, in parliament, or amongst the public.
“I think it would be very difficult and I think, if it came down to the government saying consciously, ‘well, we’ll just have to do that’, I don’t think there would be a lot of support for it,” Mr Gauke told the BBC.
“I would be very surprised if the prime minister went down that route.”
Underlining the deep divide in government, Mr Gauke’s comments came as a Treasury minister issued a “call to action” to businesses to get ready for the risk of crashing out.
Mel Stride told firms to “get a customs agent on board” and to consider software they could use to make import and export declarations.
On Thursday, Mr Gauke tweeted a picture of himself holding a unicorn, in a clear statement about Brexiteer cabinet ministers he has accused of “unicorn thinking” in supporting no deal.
The justice secretary, who supports the prime minister’s apparently doomed withdrawal agreement, urged MPs to accept “greater responsibility” by setting out other options if parliament throws out the agreement next month.
Mr Gauke said: “I think making a conscious decision to proceed with no deal would not be the responsible course of action and I think we would have to look at what other choices were available to us.”
And he added: “Although parliament clearly doesn’t want no deal, it’s not clear that there is a majority for a specific course of action to stop no deal.”
On Thursday, senior Tory and Labour MPs joined forces in an attempt to block no-deal Brexit – they started by tabling an amendment to the Finance Bill.
It would prevent the enforcement of any new taxes earmarked for no-deal preparations without the consent of the Commons – with other, similar ambushes to follow.
The move comes after Ms May’s decision to swing back towards a willingness to crash out of the EU, despite her own civil servants warning of food and medicine shortages and chaos at ports.
The cabinet agreed £4bn of extra government spending on preparations as the EU also ramped up its own measures, with less than 100 days until the UK is due to leave the bloc.
On Wednesday, the British Chambers of Commerce, the Confederation of British Industry, manufacturers’ organisation the EEF, the Federation of Small Businesses and the Institute of Directors issued a joint statement warning it was too late to avoid damage from no-deal Brexit.
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