Downing Street aides directly asked hard-Brexit Conservatives at Chequers on Sunday whether Theresa May’s resignation as prime minister would be enough to get them to endorse finally the exit deal struck with the European Union, it has emerged.

The afternoon summit at the prime minister’s country retreat was carefully choreographed so that Boris Johnson, Iain Duncan Smith, Jacob Rees-Mogg and other Tory rebels present ended up in one-to-one chats with key No 10 staffers when the main meeting periodically broke up.

A source said that in those private conversations several aides to the prime minister present asked whether it would help them vote for the controversial Brexit deal if May were to quit. “It didn’t look like a coincidence; aides like this are not meant to think for themselves,” they added.

The prime minister made no mention of resigning in the three-hour rolling meeting at the country retreat described as “like a royal levee”, although the idea was at one point put to her by Rees-Mogg and, according to some accounts, Duncan Smith. May did not respond.

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Downing Street had hoped to pick off some of the rebels attending, but did not appear at first to have made much progress, and the meeting broke up inconclusively without any breakthrough.

Others present were Dominic Raab and David Davis, both former Brexit secretaries, Steve Baker, the vicechair of the backbench European Research Group, and the May ally and former cabinet minister Damian Green.

Cabinet ministers present included David Lidington, who is in effect May’s deputy, Michael Gove, the environment secretary, and the chief whip, Julian Smith. The team of aides was led by May’s chief of staff, Gavin Barwell.

Intense speculation is circling at Westminster as to whether May will name a departure date in a final attempt to get her Brexit deal approved, amid chatter in Tory circles that government whips are beginning to ask MPs if that would persuade some of the 70 holdouts to change sides.

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The prime minister is due to appear at a meeting of the backbench 1922 Committee early on Wednesday evening, where she is likely to face questions about her future after a dismal period for the government in which MPs voted to take control of the Brexit process on Monday night by 329 to 302.

Of particular concern at the Chequers meeting was that Raab remained relatively silent throughout, leaving his position unclear. Johnson and Raab are locked in a contest to be the hard Brexiter standard bearer in any future leadership contest, and each is thought reluctant to switch to supporting May’s deal if the other does not.

Rees-Mogg and Duncan Smith were considered ready to back May’s deal if they could find an appropriate justification, cabinet sources said. Two days after the summit, Rees-Mogg went public, saying he could back May’s deal rather than risk Britain’s departure from the EU being delayed or abandoned.

However, it is not thought he speaks for many colleagues in the hard-Brexit ERG, who have so far consistently opposed May’s deal. A majority of its members spoke up for maintaining a hardline position at a meeting on Monday night in Westminster.

Of the other senior Tory backbenchers attending, Davis has already voted for May’s deal once this month when it was defeated by 149 votes, while Green is a longstanding supporter. Baker remains a holdout.

Downing St insiders said it was not the case that the idea of May’s departure was canvassed as part of a pre-arranged exercise. “There was no such operation that took place in any sense,” a source said.