WASHINGTON—A measure of U.S. services industry activity surged to a record high in October likely as declining COVID-19 cases boosted demand, but businesses remained burdened by snarled supply chains and the resulting exorbitant prices. The Institute for Supply Management said on Wednesday its non-manufacturing activity index vaulted to a reading of 66.7 last month. That was the highest since the series started in 1997 and followed a 61.9 reading in September. A reading above 50 indicates growth in the services sector, which accounts for more than two-thirds of U.S. economic activity. Economists polled by Reuters had forecast the index edging up to 62.0. The summer wave of coronavirus infections driven by the Delta variant has subsided, encouraging more consumption of services like air travel and dining out. The survey’s measure of new orders received by services businesses soared to a record 69.7 last month from 63.5 in September. Spending is …