Conservative MPs have openly discussed methods of ousting the prime minister at a private meeting of hardline Brexiters.

At the gathering on Tuesday night of the European Research Group (ERG) of more than 50 Eurosceptic MPs, sources said MPs in the Thatcher room in Portcullis House discussed the timing of a possible confidence vote in the prime minister if she did not ditch her Chequers plan.

One said there was “an utter lack of dissent” in the room about the need to replace May. “They ran through the ‘how to’ options. It was not a question of ‘should do’,” they said.

After a feverish night of mounting dissent in Westminster, the environment secretary, Michael Gove, called for calm. “The critical thing is we need to make sure there is unity in the Conservative party behind the prime minister,” he told BBC Radio 4’s Today programme on Wednesday.

Quick Guide Will the Chequers agreement survive? Show Who dislikes the Chequers agreement and why? Noisiest in their opposition are Tory Brexiters, not least David Davis and Boris Johnson, both of whom quit the cabinet in protest. They argue that the promise to maintain a common rulebook for goods and other continued alignment will mean a post-Brexit UK is tied to the EU without having a say on future rules, rather than being a free-trading independent nation. Labour has also disparaged the proposal, expressing deep scepticism about the so-called facilitated customs arrangement system. What about the EU? Brussels has sought to stay positive, but has deep concerns about elements of the plan viewed as overly pick-and-mix, and thus potentially incompatible with EU principles. Michel Barnier, the EU’s chief Brexit negotiator, says he opposes both the customs plan and the idea of alignment for goods. He also makes plain his contention that the Chequers plan contains no workable idea for the Ireland-Northern Ireland border. But at the same time the EU has been careful to not entirely dismiss the proposals, raising the possibility it could accept some adapted version. Who supports the agreement? Officially, May and her cabinet, though even here the backing can seem lukewarm at times. Asked about Chequers, the home secretary, Sajid Javid, said it was the government’s plan “right now”, indicating alternative ideas could be considered. Is it doomed? Even May’s allies concede it will be a hugely difficult task to get the plan through parliament. Damian Green, the PM’s close friend and former de fact deputy, described the process as “walking a narrow path with people chucking rocks at us from both sides”. On the remain side of the Conservatives, the former education secretary Justine Greening called the Chequers plan “more unpopular than the poll tax”, saying May should start again from scratch. If anything can save the plan – and it’s an outside shot – it will be a combination of the hugely tight timetable and the fact that, as yet, no one else has yet produced a plan with a better chance of being accepted by parliament. What happens next? On 20 September, an informal gathering in Salzburg, Austria, will provide a snapshot of current EU thinking. Then, 10 days later, the Conservative conference could show the Chequers plan is holed below the waterline. If it survives these tests, the proposals will then reach the crucial EU summit Brussels on 18 October, with something final needed, at the very latest, in the next two months. PETER WALKER

“This is loose talk and the critical thing is we deliver on the Brexit mandate, and any diversion or distraction from that commitment means our ability to ensure that it is delivered is undermined.”

At the meeting, sources said it was younger MPs who did the bulk of the talking, and veterans of the Eurosceptic movement, including Bill Cash, Iain Duncan Smith and Bernard Jenkin, were not present.

“Possibly one of them would have formally decried open leadership talk if they had been present,” the source said.

A confidence vote would require 48 MPs to send letters of no confidence to Graham Brady, the chairman of the 1922 Committee of backbench Tories.

However, May would need only a simple majority to see off a challenge and Downing Street is confident Conservative rebels do not have the numbers to topple her. If she defeated a no-confidence vote, the prime minister could not be challenged again for another year.

No 10 hosted sceptical Tory MPs on Tuesday night for a dinner with May’s chief of staff, Gavin Barwell, and director of communications, Robbie Gibb. Guests included the fierce critics John Baron and Andrew Bridgen, who has publicly declared that he has submitted his letter of no confidence in the prime minister.

Speaking to ITV outside Downing Street, Baron said the MPs had discussed “leadership issues”. Asked whose leadership was under discussion, Baron said: “You guess.”

Bridgen said he too had raised the issue of May’s leadership. “I’m told she will get a full appraisal of comments that were made at the dinner. I hope the prime minister will take on board what she’s heard and chuck Chequers, and we can move to the super Canada free-trade deal that would best serve our exit from the European Union,” he said.

The former Brexit minister Steve Baker, a key member of the anti-Chequers campaign, has claimed 80 Tory MPs would vote against the prime minister’s plan, but said they were not trying to force a “no deal” outcome. “We are all agreed it would be preferable to leave smoothly into an agreement,” he said.

May is holding a no-deal cabinet meeting on Thursday at which ministers will discuss plans in the event of the government failing to reach an agreement with Brussels.

The prime minister has challenged Brexiters to publish their alternative plan, but ERG members appear to have struggled to agree on how to avoid a hard border in Ireland, a main sticking point in discussions with Brussels.

A plan to brief journalists about a proposed solution to the Northern Irish border was pulled on Tuesday and is now expected on Wednesday. The group’s chairman, Jacob Rees-Mogg, said it was a plan that “any reasonable person” would accept and could include tax inspectors conducting spot checks in factories on goods for export.