Business leaders have warned Theresa May that “patience is wearing thin” with the government’s indecision on Brexit, as her inner cabinet comes under intense pressure to give a clearer signal about Britain’s future relationship with the EU.

On the day cabinet ministers prepared to gather for the first of two crucial meetings, the British Chambers of Commerce released a strongly-worded statement saying that “businesses need those elected to govern our country to make choices”.

In an open letter to the prime minister, the BCC’s president, Francis Martin, and director-general, Adam Marshall, said the perception of their 75,000 member firms is of “continued division” at the top of government.

“The BCC has refrained from entering into the noisy political debate on the shape of the final settlement in recent weeks. We have instead emphasised the need for answers to the many practical questions businesses now face,” they said.

“Yet businesses need those elected to govern our country to make choices – and to deliver a clear, unequivocal statement of intent.

“The perception amongst businesses on the ground, large and small alike, is one of continued division. Even amongst the many optimistic, future-oriented firms – those who see opportunity in change – patience is wearing thin.”

The Brexit subcommittee is expected to tackle the border in Northern Ireland in the first of a pair of two-hour meetings aimed at clarifying the government’s approach, in advance of intensive talks in the coming weeks.

But senior government sources were already playing down the likelihood of significant progress this week, with one warning the most likely outcome was “more fudge”. The prime minister’s spokesman said Brexit was not discussed at Tuesday’s weekly meeting of May’s full cabinet.

The 11-member Brexit strategy subcommittee includes the chancellor and the home secretary, who would like to see the closest possible continuing relationship to the EU, and “divergers” including Michael Gove and Boris Johnson.

The shadow Brexit secretary, Keir Starmer, said: “Now is time for the prime minister to deal with the divisions in her cabinet and rethink her reckless approach.

“At every twist and turn of the Brexit process, Theresa May has put party politics above the national interest. If she ploughs on with this approach then she risks a hard border in Northern Ireland and barriers to trade that would harm the economy.”

This week’s meetings take place against the background of a fraught atmosphere in the Conservative party, after the pro-Remain MP Anna Soubry warned on Monday that the prime minister should rein in vocal Eurosceptics such as Jacob Rees-Mogg.

Soubry, who told the BBC’s Newsnight the Brexiters should be “slung out,” said she had been “amazed” at the number of messages of support she had received from colleagues – and warned May against seeking a compromise this week.

“She seems to think she can build a compromise in the Conservative party and get it through; but these people won’t concede: they have no history of that,” she said.

Centrist Tories have been alarmed at the rising profile of Rees-Mogg in recent weeks – and the Eurosceptics’ increasing tendency to flex their muscles publicly, not least in forcing Downing Street to distance the prime minister from remarks by Philip Hammond that he hoped Britain would diverge “modestly” from the EU after Brexit.

Jeremy Lefroy, another Tory moderate, said, “it’s all in a state of flux at the moment; a lot of people are very concerned about the way things are going.”

When Justine Greening, who stepped down as education secretary in last month’s reshuffle, was asked on the BBC’s Daily Politics if she could imagine serving in a Conservative government of which Rees-Mogg was leader, replied, after a pause, “that might be a bit of a stretch”.

Rees-Mogg convened a meeting of his backers from the European Research Group on Tuesday evening. They were cheered by a statement issued by Downing Street earlier in the week restating the government’s intention of leaving the customs union, after it was widely reported that No 10 was working on a compromise measure that would involve a continued customs partnership.