Plunging out of the European Union in two years without a new trade deal would open up a Pandora’s box for Britain’s businesses, Paul Drechsler, the president of CBI, has warned.

As Theresa May prepares to trigger the formal talks process for leaving the EU, Drechsler used a speech at Mansion House in the City of London on Thursday night to warn that the two-year article 50 process would be a “roller-coaster” for businesses trying to plan for the future.

The prime minister has said that at the end of the two-year process, no deal would be better than a bad deal, and the Brexit secretary, David Davis, has warned his cabinet colleagues to draw up contingency plans in case Britain has to exit without a deal and is forced to trade with the rest of the EU on less preferential World Trade Organisation terms.

But Drechsler said the consequences for some companies would be so dire it was impossible for them to prepare.

“Here in the UK and across the continent firms are worried about this ‘worst-case scenario’. Some are getting ready for it to reduce economic damage. Some won’t prepare because they’re hoping for a deal. But in reality many firms can’t prepare because the cost of change is simply too high to even consider it,” he said.

Drechsler told the Guardian he had become increasingly concerned about suggestions that leaving without a new trade deal with the rest of the EU would be manageable.

“There are now a number of people around who seem to think no deal would be fine; WTO rules would be fine. The more I hear that, the more I worry that that becomes the narrative,” he said.

Recent Guardian analysis suggested reverting to WTO trading rules – an outcome sometimes referred to as “hard Brexit” – could cost firms up to £6bn in increased tariffs alone.

Drechsler said up to 90% of the value of Britain’s exports to the EU would be hit either by export tariffs, or other non-tariff barriers such as burdensome regulations or costly customs checks.

Amid concerns that the government is not thinking through the practical consequences for businesses of dropping out of the EU without a deal, Drechsler gave a series of examples to ram home his argument in his Mansion House speech.

“Imagine you’re a small cosmetics firm in Stockport and shops in France sell your products. No deal? Without an EU office it’s illegal for those French shops to sell your products. A loss for you and for them.”

“Imagine you’re a German tourist in Edinburgh and you use a credit card to pay for a hotel. No deal? The German bank may not be able to make that payment, disrupting business in both countries.

“Or imagine you’re a chemicals company in Leeds and you have systems that track your ingredients from Poland. No deal? You’ll face delays and higher costs getting supplies. Hurting your Polish customers too.”

May made clear in her Lancaster House speech in January that she hopes to strike a new trade deal with the EU, by the end of the two-year negotiation process, which will make exporting goods into the single market, “as frictionless as possible”.

But the negotiations are expected to be complex, and involve a series of other issues, including the future status of EU nationals in the UK, and how much Britain should pay towards its share of future EU liabilities, such as pensions costs. Senior figures in Brussels believe this “divorce bill” should be up to €60bn (£51bn).

“Right now, it feels like we’re just reaching the top of the article 50 rollercoaster. Any minute now, maybe next week, maybe the week after that we’ll suddenly drop into the twists and turns of negotiations,” Drechsler said.

He added that firms will be watching the talks closely, and had to make long-term plans about investment. “Boards have a duty to their shareholders, and it’s not an option just to sit on their hands,” he said. “For many of our great manufacturing businesses the planning horizon is three, five, 10, 20 years.”

However, Steve Baker, who chairs the influential European Research Group of Conservative MPs, said Drechsler was exaggerating the risks of falling back on the WTO, the Geneva-based institution that polices the global marketplace.

“With respect, Mr Drechsler is wrong. Economists for Free Trade have shown the right policies under WTO rules would make the UK better off. The Legatum Institute Special Trade Commission has set out, amongst other things, how to deliver an efficient supply chain under WTO rules. I would encourage the CBI to engage with them both.”

Economists for Free Trade, a campaign group previously known as Economists for Brexit, has produced a series of reports calling on the government to use leaving the EU as an opportunity to lower tariffs and become a “true global leader in free trade”.