Cabinet ministers joked that MPs seeking the perfect Brexit deal were like middle-aged swingers looking for Scarlett Johansson or Pierce Brosnan, during a meeting in which Theresa May confirmed the delayed meaningful vote would take place next Tuesday.

Downing Street would not say if the cabinet meeting had discussed whether the prime minister was still likely to lose the poll, with more than 100 Conservative MPs committed to voting down her deal.

The focus was on seeking new assurances from the EU on the Irish backstop and on the merits of the prime minister’s arrangement, May’s spokesman said.

During the meeting, the first of the new parliamentary term, one source said the environment secretary, Michael Gove, suggested MPs hoping for a better deal were like “mid-50s swingers” wishing Johansson would turn up to one of their parties. “Or Pierce Brosnan,” said the work and pensions secretary, Amber Rudd.

Later in the discussion, the justice secretary, David Gauke, compared Labour’s Brexit position to Johansson turning up on a unicorn, one Whitehall source said.

Much of the cabinet meeting was dedicated to discussing the difficulties of a no-deal departure from the EU, led by the Brexit secretary, Stephen Barclay. Concerns about security and illegal immigration were raised by the home secretary, Sajid Javid, and Rudd, his predecessor at the Home Office.

May announced the final vote on the Brexit deal would take place on 15 January after five more days of debate. It is understood the government hopes it will be, in effect, a continuation of the postponed debate on the motion that was put down before Christmas, rather than a new motion, but that is contingent on whether the Speaker agrees to it.

MPs who spoke in the debate before Christmas are to be permitted to speak again in the days ahead.

On Wednesday, Barclay will open the debate, which will be closed by the prime minister next Tuesday. May is still fighting for concessions from the EU over the Irish backstop, having promised legally binding assurances that the insurance option to keep the UK in an effective customs union would be temporary and used only in the most severe circumstances.

The lack of progress with Brussels may mean MPs restart the debate without any material change to discuss.

Downing Street said there would be something on offer “before the vote” and indicated MPs would have some time to debate whatever change came about.

May’s spokesman said the prime minister had “reaffirmed” that the UK was not intending to seek an extension to article 50 to allow more time to reach an acceptable deal. “There are people in the EU discussing this issue, but that is not the position of the UK government,” he said. “We will not be extending article 50.”