The Conservatives face a “catastrophic split” if Theresa May relies on Labour votes to push her Chequers plan through parliament, one of the prime minister’s most persistent critics has warned, as the conflict within the party over Brexit intensified.

After a weekend dominated by coverage of Boris Johnson’s views on the UK’s withdrawal from the EU, and his tangled personal life, the former junior Brexit minister Steve Baker used an interview to mark 200 days before departure to argue May must take a different approach.

Baker, who quit in July over Chequers, said at least 80 Conservative MPs would be willing to vote against the plan, which Eurosceptics argue ties the UK too closely to the EU on regulation and alignment, hampering future bilateral trade deals.

The issue is expected to dominate the Conservatives’ annual conference at the end of the month, with MPs from the hard-Brexit-backing European Research Group (ERG), which Baker formerly chaired, hoping to sink the Chequers proposal.

“If we come out of conference with her hoping to get Chequers through on the back of Labour votes, I think the EU negotiators would probably understand that if that were done, the Tory party would suffer the catastrophic split which thus far we have managed to avoid,” Baker told the Press Association.

“We are reaching the point now where it is extremely difficult to see how we can rescue the Conservative party from a catastrophic split if the Chequers proposals are carried forward.

“It is absolutely no pleasure whatsoever to me to acknowledge that, but I look at the mood of colleagues and the mood of the Conservative party in the country and I am gravely concerned for the future of our party.”

While it is widely acknowledged that Johnson, who also wants May to abandon the Chequers plans, is seeking to position himself as the next prime minister, Baker said he was not advocating a change in leadership. “Time is running awfully short for anyone who thinks a leadership contest and a general election is a good idea,” the Wycombe MP said.

The justice secretary, David Gauke, disputed Baker’s assessment. Asked by Sky News if Baker’s view was accurate, he said: “No, I don’t think it is.”

Gauke castigated Baker and fellow Eurosceptics for not having a coherent plan of their own: “This is a process that is going to require compromises from all sides. And I think it is really important that we go forward with the Chequers proposal. Frankly, there isn’t an alternative that has been put on the table by the critics of Chequers. We haven’t had an alternative set out.”

Gauke was similarly critical of Johnson after a furore over an article by the former foreign secretary on Sunday, in which he argued May’s Brexit plans amounted to “a suicide vest around the British constitution”.

“I don’t think his comments yesterday were well judged,” Gauke said. “And, returning to the substance, I don’t think he’s set out an alternative approach to Brexit, in contrast to the Chequers plan. This is a time where we have to seriously address the issues in front of us, have a serious plan to deal with the situation. The prime minister is a serious politician who has set out serious plans.”

Asked later by BBC Radio 4’s Today programme as to whether he could serve under Johnson, Gauke said there was no vacancy, adding: “I’m probably not a natural Boris supporter.”

The former education secretary Nicky Morgan likened the “suicide vest” comment to a previous Johnson article in which he likened Muslim women wearing the niqab to “letterboxes”. Both were “deliberately incendiary language which just masks the ability to debate the issues”, she said.

Morgan added: “Boris has to make a decision – I think he’s sort of made it. He’s either a journalist or a he’s a politician. He knew exactly what he was doing when he was using that language.”

Baker and his ERG allies are seeking a so-called Canada-plus deal, which would be based around free trade, but with notably more limited alignment to EU rules.

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The ERG has been drawing up its alternative Brexit plan based on this. A draft leaked over the weekend showed it also called for significant tax cuts, something strongly argued for by Johnson in his weekly column for the Daily Telegraph on Monday.

Baker said the ERG had decided to hold back on publication of its detailed plan in order to focus on a plan to avoid a hard Irish border after Brexit, which he said was the “key to the gate” to a satisfactory agreement.

Another ERG member, the Tory MP Simon Clarke, told Today he believed this was possible, adding: “The Northern Irish border issue is one that has been greatly exaggerated and abused. I think, for Irish domestic political reasons and by the EU itself. I think there are good reasons to believe that if you want to solve the problem then you can.”