Business leaders have written to the prime minister, Theresa May, urging her to avoid opting for hard Brexit.

In an open letter, they said leaving the UK without unfettered access to the single market would cause such grievous damage that it should immediately be ruled out as an option.

“The government must make sure that the terms of the deal to leave [the EU] ensure stability, prosperity and improved living standards,” they said in the letter, released on Friday.

Among the signatories to the letter were Carolyn Fairbairn, the head of the Confederation of British Industry (CBI), and Chris Southworth of the International Chambers of Commerce (ICC). It was also signed by Terry Scuoler, the boss of the Engineering Employers’ Federation (EEF) – which represents manufacturing firms – and Julian David of techUK, which speaks for the technology industry.

At the Conservative party conference, the prime minister indicated that accessing the single market would be a target during the Brexit negotiations. But she suggested she was unwilling to allow the continuation of freedom of movement – which EU leaders are expected to demand – to attain it.

But the heads of some of the UK’s biggest trade bodies have urged her to prioritise single market access, which they said was “vital to the health of the UK economy, especially to our manufacturing and service sectors”.

They wrote: “Leaving the EU without any preferential trade arrangement and defaulting to trading by standard World Trade Organisation rules would have significant costs for British exporters and importers, as well as those in their supply chains.”

They said that 90% of the UK’s goods trade with the EU would be “subject to new tariffs” that would mean “20% in extra costs for our food and drink industry and 10% for our car producers”.

“Every credible study that has been conducted has shown that this WTO option would do serious and lasting damage to the UK economy and those of our trading partners. The government should give certainty to business by immediately ruling this option out under any circumstances,” it read.

“The UK voted to leave the EU but not, as the chancellor said, to cause living standards to decline. We want a Brexit that safeguards future prosperity for everyone across the UK.”

The business leaders also called for a transitional period for the shift to be negotiated, rather than leaving UK businesses to deal with a “cliff edge” when the country leaves the EU.

“There is a wealth of evidence to suggest EU negotiations will not be completed within the article 50 two-year timeframe. Many areas of regulation now up for discussion are highly complicated; whether in financial services, data protection regimes or the interconnection of energy supplies,” the letter said.