However, even this preferential agreement might be out of reach for the U.K. Switzerland’s special EU market access is based on its allowing citizens of EU member countries to live there, but this deal could unravel; Switzerland is preparing to implement its own immigration caps by 2017, following its own referendum in 2014.

As a result, negotiations on giving Swiss exporters even better access to EU markets have been frozen and some existing Swiss EU trading rights ultimately might be lost. The same fate could face a U.K. government determined to impose EU immigration caps.

If the EU plays hardball on the immigrant-worker issue, the U.K. might have to accept the basic World Trade Organization member-state standards for trade with the EU, and duties then could be applied.

David Bailey, professor of industrial strategy at Aston University, warns of a “big uncertainty” for the sector following the U.K.’s vote to leave the EU. Without a deal he fears a return to the days when stiff tariffs were the norm. “What we don't want in two years’ time is to go back to (WTO) rules which involve 10% tariffs on car exports.”

Indeed, under WTO trading standards, 10% duties would be applied on almost all U.K. vehicle exports to the remaining EU, along with 3.7% duties on exported firefighting vehicles; 19% on chassis fitted with engines; 4.5% on bodies (including cabs); and 3% on bumpers, brakes, transmissions, axles, wheels and suspension systems.

Any new duties could be damaging to U.K. exporters who rely heavily on EU markets, figures released by the U.K.’s Society of Motor Manufacturers and Traders indicate.

The U.K. exports 57.5% of the cars it makes to the EU, according to the SMMT. Quoting figures for 2015, the industry group says Jaguar Land Rover produces 500,000 cars a year in the U.K., of which 20% are exported to EU countries; Ford makes 1.6 million engines annually and exports 57% of them to the EU. BMW makes 250,000 engines, with 56% bound for the EU.

BMW’s Mini subsidiary makes 220,000 cars in the U.K., of which 37.5% are exported to EU countries; of Honda U.K.’s 140,000 annual builds, 40% are exported to the EU; Nissan’s yearly output of 500,000 sees 76% shipped from the U.K. to the EU; Toyota’s annual U.K. production is 180,000 cars, 75% of which go to the EU; and General Motors’ Vauxhall brand sees 80% of its 120,000-unit annual output exported to EU countries.

While more than 40% of components purchased by U.K. automakers are imported from EU countries, the region is a key source of transmissions, axles, springs, valves, brakes, drums, engines, engine parts, cylinder heads, pistons, tires, shock absorbers, filters, gaskets, gears and other auto parts.

There are 2,049 businesses in the U.K. automotive supply chain, the SMMT says. The region makes 2.3 million engines a year including the 1.6 million built by Ford, whose Dagenham facility supplies diesel engines for all of Ford of Europe.