Britain’s biggest business organisation will make an urgent plea to Theresa May this week to come forward with clearer plans for Brexit to avoid further crippling uncertainty and serious damage to the economy.

In a speech on Monday to its annual conference, the president of the Confederation of British Industry, Paul Drechsler, will insist that the UK must retain its “privileged” access to the EU single market, keep its borders open to European talent, and agree lengthy transitional arrangements with the EU, to stop businesses falling of a “cliff edge” on the day the UK leaves.

The warning, before Philip Hammond’s first autumn statement , is a sign of growing frustration among business leaders at the government’s refusal to spell out its intentions on the UK’s involvement with the single market and customs union.

May and Hammond say they cannot give a “running commentary” or reveal their negotiating hand before talks begin with the EU once article 50 is triggered, which they “remain committed to ... by the end of March next year”.

It will also be seen as a cry for help, amid signs that EU leaders are increasingly resigned to delivering a “hard Brexit” for the UK – which will mean leaving the single market – because May and her ministers refuse to compromise over EU rules on free movement. There is also alarm among CBI members at perceived anti-business rhetoric and policy ideas emanating from No 10, such as plans to put workers on company boards.

In his speech, Drechsler will say that businesses are completely committed to making the best of Brexit. But he will make clear that there will be untold damage unless access is retained to the single market as part of a “smooth Brexit” process. In particular, he will emphasise the need for a period of transition after 2019, during which the UK remains tied into the single market and its rules, in order to avoid a sudden change and the imposition of tariffs, probably under World Trade Organisation rules.

Dreschsler will welcome a decision on triggering article 50 and other moves, such as approving expansion of Heathrow airport. But he will add: “When it comes to negotiations, no one understands the need for discretion better than business. We’re not asking for a running commentary – but we are looking for clarity and, above all, a plan.

“In other areas uncertainty remains. Business needs to know we won’t close our borders to Europe’s talent, or lose our privileged access to Europe’s markets. And there’s another important question: what happens on the day after Brexit, when the clock strikes midnight, and our two years’ negotiating time is up? Today, businesses are inevitably considering the cliff-edge scenario – a sudden and overnight transformation in trading conditions.”

However, Professor Tim Congdon, a former Treasury adviser and Ukip candidate, said MPs were right to push for leaving the single market to grab the opportunity of trading more freely with the rest of the world.

Disputing claims that the manufacturing and agricultural industries could be wiped out by cheap imports once outside the single market, Congdon said: “There is no reason why manufacturing cannot flourish outside the EU, though there is likely to be a different pattern of manufacturing.

“Singapore is the clearest example of a free market economy and it has a larger manufacturing industry as a proportion of the economy than the UK does.”

The hard-hitting intervention from Dreschsler came as it emerged that the government was warned in a report it commissioned in 2013 that the cost of leaving the Customs Union would be crippling for businesses. The economic “think-net” the Centre for Economic Policy Research, in a submission to the government’s balance of competences review, calculated that the cost of complying with new rules for trade would range from 4% to 15% of the cost of goods sold. Open Britain, a pro-European campaign organisation that includes Remain group politicians, has calculated this would amount to a cost of £12.7bn for exporting businesses.

Outside the Customs Union, UK exporters would face additional costs from Rules of Origin rules, which compel exporters to determine where a product originated. The common external tariff that operates in the EU means goods from outside can travel freely within the union once that tariff has been paid.

A mobile phone currently imported into the UK from China can be re-exported to the rest of the EU without having to pay any more tariffs. This is not true for goods that enter the EU via the EEA or via other countries with which the EU has a free or preferential trading relationship, because they do not share the EU’s common external tariff.

Anna Soubry MP, a leading supporter of the Open Britain campaign, said: “Brexit is supposed to herald a bonfire of bureaucracy, but leaving the Customs Union would leave British firms mired in expensive additional red tape.

“The government’s own figures suggest a multibillion-pound bombshell for British businesses. Before slapping them with that kind of bill, we need concrete evidence that leaving the customs union will make Britain better off.”