Chris Grayling has denied there is a “void” in government over Brexit amid a series of reports about supposed plots by MPs to take control of the process.

But the transport secretary repeatedly refused to say what Theresa May would do if her plan is defeated next week.

With the prime minister arguing it would be a “catastrophic and unforgivable breach of trust” for MPs to vote down her proposals on Tuesday, Grayling, one of May’s key allies, insisted there was a coherent plan B.

“I don’t think it is a void at all,” he told Sky News’s Sophy Ridge on Sunday programme. “The government’s coming forward with a proposal for the nation, to parliament, which says ‘this is what we think is the best compromise deal that enables us to leave.’

“It does so in a way that recognises that the nation is pretty divided on this issue.”

But Grayling refused to say what might happen if, as widely expected, MPs vote heavily against May’s plan.

“Let’s cross that bridge if and when it happens,” he said. “Right now her focus, my focus, the government’s focus is on convincing people that actually this is the best thing to do, it’s the right option. It’s the most likely to deliver Brexit.”

Pressed again on whether a backup plan even existed, Grayling added: “I’m not going to get into will we do this, will we do that, will we do the other. The important thing is to say to fellow MPs: those concerns are out there, and they’re big concerns.”

Two days ahead of the vote, May wrote in the Sunday Express that the Commons would face the “biggest and most important decision that any MP of our generation will be asked to make”.

May wrote: “You, the British people, voted to leave. And then, in the 2017 general election, 80% of you voted for MPs who stood on manifestos to respect that referendum result. You have delivered your instructions. Now it is our turn to deliver for you.

“When you turned out to vote in the referendum, you did so because you wanted your voice to be heard. Some of you put your trust in the political process for the first time in decades. We cannot – and must not – let you down.

“Doing so would be a catastrophic and unforgivable breach of trust in our democracy. So my message to parliament this weekend is simple: it is time to forget the games and do what is right for our country.”

Her plea comes ahead of a likely tumultuous week for May and her government, as speculation swirls about the plans of backbench MPs to further wrest control of the process away from the prime minister.

Last week, an amendment led by the Tory former attorney general Dominic Grieve was controversially allowed through for a vote by the Speaker, John Bercow. It means May must present a new Brexit proposal within three working days if her plan is defeated.

Reports in several newspapers said Grieve held talks with Bercow ahead of the Speaker’s decision, with the Sunday Times talking of a “very British coup” by anti-Brexit backbenchers to thwart the process.

This idea was dismissed by the remain-backing Conservative MP Anna Soubry, who tweeted that the idea of a coup was a “nasty smear” encouraged by Downing Street.

Looks like #SundayPapers @10DowningStreet has engaged in nasty smear tactics against outstanding Parliamentarian #DominicGrieve & MPs putting country before party @ChrisLeslieMP @NickBoles to scare #Conservative collegues from voting against the PMs #Brexit “deal” #FakeNews — Anna Soubry MP (@Anna_Soubry) January 13, 2019

Asked about the idea of a plot by backbench MPs, the Brexit secretary, Stephen Barclay, argued that there was a real chance it could stop the departure process.

Recent events in the Commons had shown “that the uncertainty in terms of what will happen in the house has increased”, he told BBC One’s Andrew Marr show.

“So those on the Brexiteer side seeking ideological purity with a deal are risking Brexit, because there is a growing risk that events could unfold in ways that mean they are leaving the door ajar to ways that increase the risk to Brexit.”

In his interview, Grayling reiterated his warning that stopping Brexit could boost the far right, a view which prompted condemnation on Saturday.

“My concern is that we will have, in the aftermath of a decision not to go ahead with Brexit, what we will have is the arrival in this country of the kind of populist politics on the extremes that we are seeing in most other European countries,” Grayling said.

“I do not want that, the emergence of the populist parties that were are seeing in most European countries now, in this country, because we’ve turned round to the 17.4 million people who voted to leave and simply said to them: ‘Look guys, sorry, we’re not leaving after all.’”