LONDON—British businesses have reported a sharp rise in recruitment difficulties within the space of just a few weeks—partly as a result of a continued lack of European Union workers, official figures showed on Thursday. Some 41 percent of companies with 10 or more staff reported greater than usual recruitment challenges in the two weeks to Sept. 5, up from 32 percent in early August, the Office for National Statistics (ONS) said. Around a quarter of businesses with recruitment difficulties named a reduced number of EU applicants as a factor, rising to almost half in the transport and storage sector, where a lack of truck drivers has led to widespread delivery bottlenecks. Labour shortages were most widespread in hospitality, followed by water utilities, healthcare and construction. Britain introduced new immigration rules on Jan. 1 which require most EU workers not already living in Britain to get work visas, something that can …