Boris Johnson warned on Saturday that Britain was “on the verge of making a historic mistake”, as Theresa May arrived in Brussels to sign a Brexit deal that cabinet ministers believe will soon be blocked by parliament.

The prime minister is expected to approve the deal on Sunday despite growing certainty among allies and critics alike that she has insufficient support among MPs. She also faces a threat from the DUP, the Northern Irish party propping up her government, which could pull the plug on its support unless there is a rethink of a deal that it has branded “pitiful and pathetic”.

On Saturday, as he sought to steel DUP resistance to the deal and to parry Downing Street’s attempt to woo the party’s 10 Westminster MPs, Johnson delivered a provocative address at the party’s conference in Belfast, filled with eclectic references ranging from bendy buses to Star Wars, Van Morrison, former Venezuelan president Hugo Chávez and the Titanic.

“If you read the withdrawal agreement, you can see that we are witnessing the birth of a new country called UK(NI) or Ukni,” the former foreign secretary said. “Ukni is no longer exclusively ruled by London or Stormont. Ukni is in large part to be ruled by Brussels.”

Insisting that another attempt should be made to draw up a deal, Johnson said the UK should withhold half of the £39bn divorce settlement with the EU until a free-trade agreement was agreed by the end of 2020. He also said that the so-called backstop, a measure intended to avoid a hard border on the island of Ireland, would cleave Northern Ireland from the United Kingdom.

“We need to junk the backstop,” he said. Johnson also repeated his call for a bridge to be built between Scotland and Northern Ireland.

The criticism of May’s deal did not stop there. Nigel Dodds, deputy leader of the DUP, called the deal “pitiful and pathetic”.

In her keynote address, DUP leader Arlene Foster said the prime minister was “genuine” in not wanting to harm the union. However, she reiterated the party’s opposition. “We could not support proposals that would open the possibility of divergence in either customs or regulatory measures between Great Britain and Northern Ireland,” she said.

Opposition to the Brexit proposals is also building within May’s cabinet. The Observer understands that serving ministers are already planning to try again to demand changes to the deal once it is voted down by the Commons, in a vote expected next month.

Arlene Foster speaking during the DUP annual conference. Photograph: Michael Cooper/PA

Scores of Tory MPs are still vowing to vote against the deal, despite desperate attempts by No 10 to convince them that it is the best and only agreement Britain will be offered.

In an interview with the Observer, David Lidington, the Cabinet Office minister, urged his colleagues to get behind the prime minister, saying the backstop was designed to kick in only if no other solutions were found for keeping the Irish border open. He said the idea that the EU was involved in a plot to keep the UK locked in was laughable.

“I know some of my colleagues have worries that this is a deep plot from Brussels to trap us,” he said. “All I can say is, go and talk to people, whether in Brussels or in national governments. You put that point to them and they just snort with derision or break into laughter. As they see it, the backstop gives the UK access to the EU’s precious single market without the UK paying into the budget and without the UK accepting free movement, and without the UK accepting all the obligations that come from full EU membership.”

Lidington said May’s deal was the only one on offer and the only one that could unite the nation after a divisive referendum. “It provides a way in which to bring the country together,” he said. He warned those campaigning for a second referendum that it would only “prolong the uncertainty”.

“I don’t think anything is certain about a hypothetical second referendum, except that it would not be decisive. It would divide people all over again. It would leave whoever came out on the losing side still resentful. We owe it to the British public and British business to take a decision, get behind this deal and make it work, because I don’t see a better one on offer.”

Meanwhile, hardline pro-Brexit former cabinet ministers joined what appeared to be a coordinated effort to torpedo May’s plan and undermine her big moment – calling on her to renegotiate the package and, if this is unsuccessful, prepare the country for a no-deal outcome.

David Davis, the former Brexit secretary, said that what the prime minister had negotiated was worse than no deal. As far as he and other Tory Brexiters were concerned, it was “now a case of new deal, or no deal”. He said May’s plan had “a near-zero chance of getting through the House of Commons” when a meaningful vote was held, probably in the second week of December.

Former international development secretary Priti Patel also called on May to renegotiate the deal, which she said she would definitely vote against in its current form. “We have still got time to get it into a better place and make it more in line with the prime minister’s previous speeches and the Conservative manifesto,” she said.

“You can’t go in one direction with one vision and offer lots of reassurance and then come up with something completely different. People are not completely stupid. We are on the verge of losing all faith in our politics and politicians.”

Prominent Tory Remainers also attacked the deal as a betrayal of the British people. Former cabinet minister Justine Greening, who backs a second referendum, said it would damage the UK and in particular let down young people. “This deal fixes nothing but risks everything,” she said. “It leaves Britain’s economy and the union in a permanently weak position.”