LONDON—Immigration to the U.K. from the European Union slowed sharply in the year through March, while business investment in the second quarter was flat, highlighting how last year’s Brexit vote is weighing on the British economy.

The figures come as the U.K. prepares for a fresh round of negotiations with Brussels over the terms of its exit from the EU. Data confirmed that growth in the U.K. in the second quarter was weaker than Germany, France and Italy, as British consumers grapple with rising prices fueled by a weak...