Every week, workers in a warehouse near the Sardinian port of Cagliari pile two pallets with local specialties such as fresh artichokes, fiore sardo cheese, and bottarga fish eggs. The pallets are loaded onto a truck for a journey across Italy, France, and the English Channel before arriving five days later at Olivo, a Sardinian restaurant in London where chefs turn the food into $30-a-plate delectables such as spaghetti with sea urchin or Sebada, a pecorino cheese fritter covered in honey.

With the coronavirus pandemic, Olivo and its sister restaurants in the posh area near Westminster have cut the weekly order from four pallets to two. Now, Britain’s departure from the EU threatens to make the journey more cumbersome, expensive, and slower—if it’s even possible.

In Sardinia, the deliveries are packed by Olivo employees, who source the produce locally and pack smallish quantities of various foods onto the pallets. After Brexit, each individual item will have to be coded and logged in transportation documents to be checked at the border before entering the U.K., complicating the process to the point where it may no longer make sense. “I need three to four hams a week,” said Olivo owner Mauro Sanna. “I can’t buy a whole pallet.”

Like many other Italian eateries in London, the Olivo group—four restaurants, a deli, and a gelateria—is very much a product of the single market. Its staff is mostly Sardinian, able to work in the U.K. without special papers or visas. And its gourmet meals are made possible by a supply chain that extends seamlessly across national borders to the Mediterranean island. Since its founding in 1990 as a single restaurant, the group has grown to sales of 5 million pounds a year, employing about 100 people.

Although the deal between the EU and the U.K. won’t impose tariffs or quotas, it will surely create greater friction in trade. Importers and exporters will face new paperwork, and customs officials will check delivery vehicles at the border—vastly increasing the bureaucratic burden, especially for small-scale operations such as Olivo, said Sam Lowe, a senior research fellow at the Center for European Reform. “The era of mixed consignments will pretty much come to an end,” Lowe said. “It just becomes too much hassle.”

Sanna says he’ll hire an agency to negotiate customs, and he fears he may have to shut the purchasing and packing operation in Sardinia. If he does, he’ll have to import full pallets of foods such as wines, cheeses, and mineral water from larger producers and warehouse them in London. Other goods such as mozzarella, extra virgin olive oil, and canned peeled tomatoes could come from U.K. wholesalers.

But he says replacing the Sardinian specialties he imports will be more difficult. “The main reason for this set-up isn’t cost, but authenticity and quality,” he said. “It is about identity, and it will be hard to maintain that.”

He’s also worried that hiring will become harder. Until now, it’s always been easy to find enough Sardinians already living in London to keep the kitchens humming and diners happy. Post-Brexit, Europeans wanting to move to the U.K. will need a job offer to get working papers, so Sanna will need to take greater risks in hiring. “It’s hard to know if someone is good or not if you haven’t met them in person,” he said.The burden will also fall on small producers like those Sana buys from in Sardinia. These people today can easily sell their wares across Europe, but Brexit will mean more forms to fill and require more official approvals—and some will inevitably feel that’s not worth the trouble. The end result is that “costs will be much higher,” Sanna said. “And these ultimately will be transferred to customers.”