LONDON, Sept 16 (Reuters) - British businesses have reported a sharp rise in recruitment difficulties over the past month, with 41% of companies with 10 or more staff reporting challenges in the two weeks to Sept. 5, up from 32% in early August, official figures showed. The Office for National Statistics said on Thursday that recruitment difficulties were greatest in the hospitality industry, followed by water utilities and in healthcare and construction. (Reporting by David Milliken; editing by Sarah Young)