LONDON—Economic activity in the eurozone shrank markedly in January as stringent lockdowns to contain the coronavirus pandemic hit the bloc’s dominant service industry hard. With hospitality and entertainment venues forced to remain closed across much of the continent, surveys on Friday highlighted sharp contractions in the services industry but also showed manufacturing remained strong as factories largely kept working. IHS Markit’s flash composite purchasing managers’ index (PMI) for the eurozone, seen as a good guide to economic health, fell further below the 50 mark separating growth from contraction to 47.5 in January from December’s 49.1. A Reuters poll had predicted a fall to 47.6. “High infection rates are again forcing governments to extend and tighten containment measures,” said Tomas Dvorak at Oxford Economics. “The flash PMIs point to a looming contraction in eurozone GDP in Q1. We don’t expect any meaningful economic recovery before the pandemic is brought under control.” …