ROME/STOCKHOLM—Post-Brexit trade rules mean prosecco supplier Serena Wines 1881 must store bottles destined for Britain on costlier, fumigated pallets in their own corner of its warehouse in the northeast Italian town of Conegliano. The new shipment requirement is one example of the extra cost and complexity that firms across continental Europe face serving British customers since Jan. 1, adding to disruption of the COVID-19 pandemic to drive UK-EU trade volumes lower. “These first months have been hectic, hellish for everyone,” said export manager Nicola Piovesana. “Delivery times are now longer, now it takes 2 weeks to get to the (UK) client, while before it took one week at the most.” The Dec. 24 deal reached between Britain and the EU after years of wrangling over post-Brexit trade terms at least meant goods trade—roughly half the total $900 billion of annual EU-UK commerce—was spared from tariffs and quotas. But January trade …