Labour will seek immediate talks with Tory ministers who resign from the government on Wednesday – including the chancellor, Philip Hammond – in the hope of building a cross-party alliance to prevent Boris Johnson from embracing a no-deal Brexit.

The plans, revealed to the Observer by shadow Brexit secretary Keir Starmer, underline the extent of opposition the probable next prime minister will face from across the House of Commons if he fails to negotiate a new Brexit deal that can pass through parliament by late autumn.

Johnson, firm favourite to win the Tory leadership contest on Tuesday and enter No 10 the following day, has promised to deliver Brexit on 31 October come what may, which means he will be prepared to leave without a deal if necessary.

But after MPs last week voted by a majority of 41 to make it more difficult for a new prime minister to force through no deal by shutting down parliament, further cross-party plans are being made to block that option.

Starmer will approach Hammond and others, including the justice secretary, David Gauke, for talks on how to prevent no deal this week. Writing in today’s Observer, Starmer says parliament must be put on a “war footing” to prevent a no-deal outcome, with party allegiances put aside in the national interest.

“On Tuesday morning some ministers will sit around the cabinet table for the last time,” Starmer says. “They know very well the dangers of no deal. They will have been briefed about what it would mean for jobs, the economy, our public services and the union. They will have seen the advice and read the evidence.

“After they have resigned this week, I will want to work with all those former ministers who, like me, want to ensure parliament can stop a disastrous and chaotic exit from the EU.”

Starmer says Johnson and his rival for the Tory leadership, the foreign secretary, Jeremy Hunt, have competed over recent weeks in an “arms race towards a more and more extreme form of Brexit. Deeper red lines, even more ludicrous promises, but absolutely no coherent or workable plan for the country.”

Last week the government’s independent forecasting body, the Office for Budget Responsibility, said a no-deal Brexit would plunge Britain into a recession that would shrink the economy by 2%, push unemployment above 5%, and send house prices tumbling by around 10%. It said the result would be a year-long downturn that would increase borrowing by £30bn a year.

Hammond suggested in an interview with the French newspaper Le Monde and Germany’s Süddeutsche Zeitung last week that he could vote to bring down a Tory government that sought to drive through no deal against parliament’s wishes. Asked to rule out supporting a no-confidence motion in a Johnson government, the chancellor responded: “I do not exclude anything for the moment.” He added: “I will do everything in my power from my position to make sure that parliament blocks a Brexit without agreement.”

The chancellor has also expressed concern about spending pledges and promises to cut taxes made by both Hunt and Johnson during the leadership contest, urging them to “stop and think” before announcing measures that the country will in all probability not be able to afford.

Johnson will also come under intense pressure over whether or not to press ahead with the proposed HS2 rail project after it was reported that the costs could surpass the current budget of £56bn by almost £30bn. According to a report in the Financial Times, the chairman of the project, Allan Cook, has written to Bernadette Kelly, the permanent secretary at the Department for Transport, to warn that the high-speed line from London cannot be finished within the official £56bn limit.

The paper reported that, according to Cook’s preliminary findings, the project’s final cost could spiral to between £70bn and £85bn.

A source close to the project told the newspaper the costs had increased because of a “combination of poor ground conditions found during the surveying work, the costs of engineering a railway to a very high specification, and the further additional costs of it being designed to run at even higher speeds than other comparable rail projects”. Johnson has said during Tory leadership hustings that he wants a review of the costs of the project.

Andy McDonald, shadow transport secretary, said yesterday that additional rail capacity was urgently needed, but that confidence was waning in the government’s ability to deliver HS2.

“We desperately need additional rail capacity that connects with a fully developed Northern Powerhouse rail network,” he said. “These are critical elements of the advanced railway network that our country needs over the coming decades to address the climate crisis.

“We also proposed a peer review of the project, but the government said no. They should reconsider their stance and embrace that independent review. It is clear that the government and HS2 have a lot of work to do if they’re to restore confidence in this project.”