Business leaders will warn on Thursday that disputes over an EU divorce settlement worth “tens of billions of euros” risk jeopardising hundreds of billions worth of trade every year if they lead Brexit talks to collapse.

In a speech at Cambridge University, CBI director general Carolyn Fairbairn is expected to urge negotiators on both sides to focus instead on the mutual benefits of continued free trade as they begin talks that will lead to Britain’s departure from the European Union.

Leaders of the remaining 27 member states are due to meet this Saturday in Brussels for a Brexit summit that will finalise their negotiating stance and confirm EU demands for broad agreement on a financial settlement before trade talks can begin.

Though Theresa May and David Davis met lead EU negotiator Michel Barnier and EU commission president Jean-Claude Juncker at a dinner in Downing Street on Wednesday night to emphasise their common ground on a number of positions, there is mounting fear in business circles that a steep divorce bill could prove to be a damaging sticking point.

“Take a look at the numbers and you see that our long-term trading relationship is the real prize – dwarfing any potential divorce settlement,” Fairbairn will warn, according to CBI speech extracts. “A one-off EU divorce bill of, some suggest, tens of billions of euros, compared with EU-UK trade worth well over €600bn euros every year, the economic case for making rapid progress on a trade agreement is clear.”

“In just two days’ time, Europe’s leaders will be meeting at the EU summit to agree a common response to the article 50 letter,” she will add. “In these discussions it’s vital that the economics cuts through the politics. So our message to European firms and policymakers is ‘keep on talking, keep on listening’.”

At the summit, European leaders will call on the UK to make “a single financial settlement” to cover spending commitments made by previous British prime ministers and liabilities chalked up over 44 years of membership.

A commission spokesman said Juncker had a “constructive meeting” with May, where they discussed the article 50 process, as well as “the broader geopolitical agenda and issues of strategic interest to both”.

The visit was arranged before the prime minister called a snap general election last week. EU officials billed the meeting as a chance to talk over the Brexit process without getting into formal negotiations. The commission has said talks will not begin until a new British government is in office after 8 June.

Sabine Weyand, a trade expert who is Barnier’s deputy, and Martin Selmayr, Juncker’s influential chief of staff, were also at the table.

The dinner completes visits by a trio of EU institutions since May filed Britain’s article 50 notice last month. The prime minister recently met Donald Tusk, the president of the European council, and Antonio Tajani, who leads the European parliament.

The UK lobby group claims to speak for business voices across Europe in arguing that walking away without a deal on future trading arrangement would have “chilling effects” for all.

“The business community – in the UK and the EU – is united in wanting an agreement with as few barriers as possible. Yet without an agreement, we’d lose together,” Fairbairn will argue. “For both sides, leaving the negotiating table without a deal shouldn’t be ‘Plan B’ but ‘Plan Z’. Whether it’s tariffs or regulation, a no deal scenario would have chilling effects on both sides of the Channel.”

But such views of Britain’s limited trading status without an EU deal are not universally shared among business leaders, some of whom met separately at a conference in London on Wednesday to explore life after Brexit.

They were urged to follow the example of countries such as New Zealand, Chile and Estonia in adopting unilateral free trade policies, regardless of what is offered by Europe. “Whatever you do, don’t waste this moment,” said Sir Lockwood Smith, the former New Zealand high commissioner to the UK, to applause at the event, called Prosperity UK.

Davis, the Brexit secretary, also sought to reassure nervous employers that there will be a swift deal to protect the rights of EU citizens living in Britain now that exit negotiations are underway.

“The government has made it very clear it wants to secure the rights of EU nationals living in Britain at the earliest chance in the negotiations,” Davis told the conference. “I am confident we can achieve very early agreement on these issues.”

Davis insisted he was listening the concerns of business on the issue, though he hinted that immigration policy may prioritise skilled visas.

“No one wants to pull up the drawbridge. A global Britain will always want the brightest and the best,” he said. “The UK departure from the EU should not be viewed through a protectionist lens.”

The conference, organised by prominent leave campaigner and hedge fund manager Paul Marshall, struck a relatively upbeat tone about the impact of Brexit on the economy.

Even some figures with long-stated concerns about the risks of leaving the single market welcomed recent political developments. “One hopes that after the election is over, the government has clarity of mandate and more capacity to negotiate,” said Douglas Flint, chairman of HSBC.