 Born in Southwold, Suffolk, Greig made his first-class debut for Worcestershire against Hampshire in May 1920, going wicketless in the first innings but taking 4-119 in the second; his maiden first-class wicket was that of Hampshire opener Alex Bowell.He also hit 37 in the first innings, which was to remain his highest score.After another game for the county a few days later, he played his two matches for Oxford, though met with little success in either of them.