Britain risks a “disorderly crash landing” if it assumes it can safely walk away from troublesome Brexit talks, business leaders have said, in a last-ditch plea for a negotiated settlement with Europe.

As Theresa May prepares to reveal an uncompromising set of UK objectives on Tuesday, pressure is mounting on the prime minister to take a firm line with other member states and ultimately fall back on World Trade Organisation tariffs if no deal can be agreed.

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But the CBI is calling on politicians to wake up to the limitations of the WTO and dangers of a disorderly Brexit, despite the long and painful concessions that may be necessary if the UK is to obtain a replacement free-trade agreement when it leaves the single market.

“The practicalities of a disorderly crash-landing need to be understood,” said Carolyn Fairbairn, director general of the CBI, in an interview with the Guardian. “We have had conversations with some of the proponents of just walking away and we will again talk to them about what we see from our members about the consequences of that.

“An exit into WTO at the stroke of midnight without the proper planning and preparation in place would be very serious for the UK economy. There are some signs that there is more conversation around that being an outcome. Our job is to demonstrate how difficult that would be because of all of these unanswered questions.”

While keen on a “implementation phase” with Europe, the CBI is also positive about prospects for a US trade deal. In the interview, carried out shortly before news of Donald Trump’s promise to do a deal with Britain, Fairbairn pointed out that the UK and US had a large reciprocal relationship with significant enough trade flows in either direction to ensure British interests were well reflected.

The risk of a disorderly Brexit has risen in recent days as EU27 leaders have insisted that even a transitional arrangement – to allow a trade deal to be negotiated after the two-year divorce talks have concluded – would still require the UK to adhere to rulings from the European court of justice in the interim.

May was widely reported on Sunday to be preparing to call for a “clean and hard” Brexit when she makes her speech at Lancaster House this week, even though the government also still favours a transitional phase to avoid the cliff edge feared by business.

“We have been listening to what business is saying about the need for certainty wherever it can be brought,” wrote David Davis, the Brexit secretary, on Sunday. “That’s why, if it proves necessary, we have said we will consider time for implementation of new arrangements.”

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But many in the Tory party believe such ambitions must be abandoned if they come at too high a political cost, not least to demonstrate tactically that Britain goes into negotiations with the option of walking away.

Michael Gove last week called for a “full Brexit, not fake Brexit” that would be completed “in months not years”. Even the relatively moderate chancellor, Philip Hammond, said this weekend in an interview with German press that the UK could aggressively compete with Europe on tax if it made a trade deal difficult, as ministers try to signal a harder-edged tone as the time for formal exit negotiations draws close.

For British business, the hardening of political opinion on both sides of the Channel is alarming, not least as the EU negotiator Michel Barnier and the Bank of England governor Mark Carney have spoken about the dangers of financial instability without a deal.

The CBI is calling on May to set open-trade with Europe as a priority when she makes her speech. “The idea of barrier-free access is an incredibly important principle for British business,” said Fairbairn. “Yes there may be a negotiation and yes, there may be trade-offs, but it is far too early for us to be saying in any way that these cease to be important and valid objectives for our economy.”

Though the business lobby is trying to seek constructive ways forward on Brexit, it also remains concerned at the continued anti-immigration rhetoric coming from politicians.

“We do have to be incredibly careful about the reputation of the UK around the world for openness and being a welcoming trading nation,” said Fairbairn. “There is no doubt that the world is watching. They are watching our every move.”

She said things had improved since talk of a register of foreign workers made at Tory party conference and that business welcomed Downing Street distancing itself from new talk of a £1,000-per-worker immigration levy last week. “We are in a significantly better place, but we need to remain hugely alive to the interpretation that is going to be placed on what we might perceive as relatively small announcements,” said Fairbairn.

The CBI is also calling for urgent clarity on the government’s objectives before members start making irreversible decisions on relocation.

“The longer that we don’t have answers to key questions like ‘what’s the new immigration model going to be?’ and ‘what is the access to our main trading partner going to be like?’ business will be forced to make assumptions and that is why clarity matters so much,” said the director general. “The next three to six months will be vital for that.”