LONDON—Early signs of disruption caused by Britain’s shift to its new, less open trading relationship with the European Union are emerging in economic data. Although the biggest problem for many companies remains the COVID-19 pandemic, details of recent surveys show that Brexit is adding to the strain on the economy. Manufacturers and services firms have been hit hard by supply chain and export disruption, according to data company IHS Markit. British factories reported the steepest increase in supplier delivery times among the six “flash” preliminary Purchasing Managers’ Index (PMI) surveys published by IHS Markit last week for France, Germany, Japan, Australia, and the United States as well as the United Kingdom. “This was almost exclusively linked to both Brexit disruption and a severe lack of international shipping availability,” IHS Markit said. Under a deal struck last month, trade between Britain and the European Union remains free of tariffs and quotas …