Business leaders are privately pushing for a new campaign to reverse Brexit as concerns mount about the viability of government plans to prevent a collapse in exports to Europe.

On Monday, the CBI launched its most sustained attack yet on the government’s Brexit strategy by calling for full customs union with the EU and single market participation, even if it means abandoning the pursuit of separate trade deals with the rest of the world.

Behind the scenes, senior figures on the CBI policy council are urging the lobby group to toughen its message still further and spell out their belief that this logic should ultimately lead to a national rethink of the decision to leave the EU, perhaps through a second referendum or an election.

While this is not the CBI’s official position, the group says it has decided to speak out about the problems of the government’s approach to Brexit after “thousands of conversations” and workshops with its members over the past two to three months.

“It’s not for us to say [whether to reverse Brexit], we are simply pointing out that you need single market access and you need a customs union,” said a spokesman. “If someone concludes that we therefore need to retest this, that’s a political decision, we are just being very practical about it.”

Government ministers reacted furiously to previews of the CBI’s evolving position over the weekend, which now directly challenges the British strategy of leaving the customs union so that new trade deals can be pursued outside a common tariff area.

The CBI director general, Carolyn Fairbairn, told an audience at Warwick University on Monday: “There may come a day when the opportunity to fully set independent trade policies outweighs the value of a customs union with the EU; a day when investing in fast-growing economies elsewhere eclipses the value of frictionless trade in Europe. But that day hasn’t yet arrived.”

The foreign secretary, Boris Johnson, responded by arguing that such a stance undermined the central goal of Brexit:

2/2 Staying in the customs union means effectively staying in the EU: the EU *is* a customs union. It means no new free trade deals, no new export opportunities, and no leading role in the WTO. — Boris Johnson (@BorisJohnson) January 21, 2018

The Department for Exiting the EU argues that Theresa May’s strategy of leaving the single market and customs union should not preclude a comprehensive free trade deal with Europe.

“The EU has said they will offer their most ambitious free trade approach and we are confident of negotiating a deep and special economic partnership that includes a good deal for financial services – that will be in the EU’s best interests, as well as ours,” said a DexEU spokeswoman.

Nonetheless, the increasing rejection of government trade policy by the very exporters who should have most to gain comes at an awkward time for Downing Street.

European leaders such as the European council president, Donald Tusk, and the French president, Emmanuel Macron, have been stepping up their twin-track approach of presenting an uncompromising opposition on “cherry picking” trade rules while welcoming the possibility of Britain changing its mind about Brexit.

Anti-Brexit campaign groups are increasingly putting their differences aside and uniting behind a push to give parliament and the electorate a chance to reconsider the decision to leave once it is clear what kind of deal the prime minister has been able to negotiate.

An internal CBI report on the future UK-EU relationship is scathing about the prospects for a “cake-and-eat-it” solution. “Government has all the right objectives on customs but – thus far – no proposals have been set forward that can deliver,” it says. “A customs union would require trade-offs on achieving an independent trade policy, but the benefits of such a policy are unproven.”

The CBI is unlikely to be able to take an overt position on a second referendum because some members remain of the view that the vote should not be revisited whatever the change in facts.

“Inevitably there are people who think the other way as well and the reason we can’t take political positions is because there are members who would be very annoyed if we did,” a CBI spokesman said. “What we are doing today is a reflection of the fact that people are quite impatient and are quite worried.”