The TUC and the CBI released a rare joint statement with their continental counterparts calling for “measurable progress”, a day after the car industry called for a Brexit deal that delivers “single market benefits” and cabinet tensions over the issue flared into the open.

The workers’ and business organisations said: “We are calling on the UK government and the EU to inject pace and urgency in the negotiations, bringing about measurable progress, in particular a backstop arrangement to avoid a hard border in Ireland.

“Decisions will be needed in June and October to finalise the withdrawal agreement and the transitional arrangement, and put economic interests and people’s jobs, rights and livelihoods first.” It added: “The cost of disagreement between the UK and the EU would be dire for firms, workers and the communities where they live.”

Earlier on Tuesday, car manufacturers said there would be no “Brexit dividend” for the industry, with investment in the sector and thousands of jobs being put at risk unless the government rethinks its red lines in negotiations.

Ministers have been forced on the defensive since the end of last week after Airbus and BMW said jobs in the UK were at risk if manufacturers could not easily import components from the EU after Brexit. But the CBI and TUC said their concern spread further, to 23 industrial sectors which want “regulatory alignment” post divorce.

They range from banking and financial services, through to energy, broadcasting and professional services all of which seek mutual recognition of each other’s regulatory systems post Brexit. Such agreement was of “utmost importance”, said the TUC and CBI in remarks approved by Frances O’Grady, the TUC general secretary, and Carolyn Fairbairn, the CBI director general.

May tried to allay some of the concerns on Tuesday by saying it is “right that we listen to the voice of business”, in a corporate summit sponsored by the Times, as she also attempted to counter some of anti-business remarks made by other cabinet colleagues over the last few days.

“We have listened carefully to the voices of business throughout, and your input has helped to shape our negotiating position,” the prime minister added, two days before she is due to head to Brussels for a European Council meeting which is likely to be dominated by arguments over migration and see little substantive progress on Brexit.

The prime minister’s remarks also amounted to a rebuke of Boris Johnson, who effectively admitted in the Commons that he had said, in response to corporate lobbying, “fuck business” at an industry event last week.

“I don’t think anybody could doubt the passionate support of this government for business,” the foreign secretary told MPs, before adding: “It may be that I have, from time to time, expressed scepticism about some of the views of those who profess to speak up for business.”

The business secretary, Greg Clark, appeared to suggest he agreed with the concerns of industry, in a sign of emerging cabinet divisions over the issue. “What [business] don’t want is a running debate... Business looks with dismay where there is disagreement. That does not inspire confidence. My approach is to be very engaged with businesses,” he said.

The former Brexit minister David Jones criticised Clark’s stance, telling the Daily Telegraph: “There is a risk he is unwittingly participating in Project Fear mark two, which is being orchestrated by EU-based businesses.”

Cabinet members were told by David Davis in the morning that the government would try to provide more details of its plans when its long-awaited Brexit white paper is published on Monday 9 July.

That will come after an away day held the Friday before at the prime minister’s Chequers retreat. All cabinet members are expected to attend the event, which will conclude with a working dinner, a move that is expected to help May because the proportion of loyalists is greater amongst the full team.

Labour accused the government of botching Brexit “by bickering amongst themselves” rather than “negotiating a sensible deal with the EU”. Rebecca Long-Bailey, the shadow business secretary, added: “Time is running out. Business, consumers and workers need certainty and workers, not endless chaos, egos and melodrama.”

The car lobby told the government on Tuesday that it needed “as a minimum” to remain in the customs union and a deal that delivered “single market benefits”. “There is no Brexit dividend for our industry,” Mike Hawes, the chief executive of the Society of Motor Manufacturers and Traders (SMMT), said.

He said Brexit uncertainty was thwarting investment and repeated calls for the UK to stay in the customs union until the government came up with a “credible plan B”.

Negotiators had to get on with the job of agreeing a deal that would put an end to uncertainty and prioritise the needs of the automotive sector, because investment was slowing and time running out, the SMMT said at a day-long summit.

BMW, which employs 8,000 people in the UK, said it needed to know by the end of the summer what the Brexit strategy was as that was when key decisions would be made.

Ian Robertson, the most senior British executive at the German firm, said: “We are not turning our backs on the UK.” But he said that any delay in Dover “would start to impact” upon manufacturing and its competitiveness. He added that BMW was not intending to move any car production to any of its other plants around the world but it would be “foolhardy” not to have “contingency ideas”.

Hawes told reporters at the International Automotive Summit in London that “signs were more ominous” for investment this year after eight years of growth.

“If we cannot cut through the fog of the uncertainty there will be casualties,” he said. “For this year are more ominous, contingency planning, job losses, investment halved to less than £350m so far year, that’s the cost of uncertainty, that that’s the price we pay for slow decision-making,.”

A spokeswoman for the Brexit department said it agreed with business leaders. “We are confident that we can make progress if both the EU and UK engage constructively,” she said.

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